Pub Date : 2022-04-30DOI: 10.1142/s1005386722000165
C. Hong, H. Kim, N. Kim, T. Kwak, Yang Lee
We study the right duo property on regular elements, and we say that rings with this property are right DR. It is first shown that the right duo property is preserved by right quotient rings when the given rings are right DR. We prove that the polynomial ring over a ring [Formula: see text] is right DR if and only if [Formula: see text] is commutative. It is also proved that for a prime number [Formula: see text], the group ring [Formula: see text] of a finite [Formula: see text]-group [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text] is right DR if and only if it is right duo, and that there exists a group ring [Formula: see text] that is neither DR nor duo when [Formula: see text] is not a [Formula: see text]-group.
{"title":"Duo Property on the Monoid of Regular Elements","authors":"C. Hong, H. Kim, N. Kim, T. Kwak, Yang Lee","doi":"10.1142/s1005386722000165","DOIUrl":"https://doi.org/10.1142/s1005386722000165","url":null,"abstract":"We study the right duo property on regular elements, and we say that rings with this property are right DR. It is first shown that the right duo property is preserved by right quotient rings when the given rings are right DR. We prove that the polynomial ring over a ring [Formula: see text] is right DR if and only if [Formula: see text] is commutative. It is also proved that for a prime number [Formula: see text], the group ring [Formula: see text] of a finite [Formula: see text]-group [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text] is right DR if and only if it is right duo, and that there exists a group ring [Formula: see text] that is neither DR nor duo when [Formula: see text] is not a [Formula: see text]-group.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81639314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000207
Bing Wang
For the cyclic group [Formula: see text] and a positive integer [Formula: see text], we study the representations of the orbifold vertex operator algebra [Formula: see text]. All the irreducible modules for [Formula: see text] are classified and constructed explicitly. Quantum dimensions and fusion rules for [Formula: see text] are completely determined.
{"title":"Representations and Fusion Rules for the Orbifold Vertex Operator Algebras Lsl2^(k,0)ℤ3","authors":"Bing Wang","doi":"10.1142/s1005386722000207","DOIUrl":"https://doi.org/10.1142/s1005386722000207","url":null,"abstract":"For the cyclic group [Formula: see text] and a positive integer [Formula: see text], we study the representations of the orbifold vertex operator algebra [Formula: see text]. All the irreducible modules for [Formula: see text] are classified and constructed explicitly. Quantum dimensions and fusion rules for [Formula: see text] are completely determined.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89370473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000220
Jicheng Ma
We investigate the orientably regular non-abelian coverings of regular maps. A complete classification of dihedral coverings of the Platonic maps for branching over faces (or, dually, vertices) is given. As a result, we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.
{"title":"On Orientably Regular Non-abelian Covering Maps of the Platonic Maps","authors":"Jicheng Ma","doi":"10.1142/s1005386722000220","DOIUrl":"https://doi.org/10.1142/s1005386722000220","url":null,"abstract":"We investigate the orientably regular non-abelian coverings of regular maps. A complete classification of dihedral coverings of the Platonic maps for branching over faces (or, dually, vertices) is given. As a result, we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75735333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000219
Ji-Ming Guo, Gege Zhang, Zhiwen Wang, Pan-Pan Tong
Let [Formula: see text] be the set of connected unicyclic graphs of order [Formula: see text] and girth [Formula: see text]. Let [Formula: see text] be obtained from a cycle [Formula: see text] (in an anticlockwise direction) by identifying [Formula: see text] with the root of a rooted tree [Formula: see text] of order [Formula: see text] for each [Formula: see text], where [Formula: see text] and [Formula: see text]. In this note, the graph with the minimal least eigenvalue (and the graph with maximal spread) in [Formula: see text] is determined.
{"title":"The Least Eigenvalue of Unicyclic Graphs with Application to Spectral Spread","authors":"Ji-Ming Guo, Gege Zhang, Zhiwen Wang, Pan-Pan Tong","doi":"10.1142/s1005386722000219","DOIUrl":"https://doi.org/10.1142/s1005386722000219","url":null,"abstract":"Let [Formula: see text] be the set of connected unicyclic graphs of order [Formula: see text] and girth [Formula: see text]. Let [Formula: see text] be obtained from a cycle [Formula: see text] (in an anticlockwise direction) by identifying [Formula: see text] with the root of a rooted tree [Formula: see text] of order [Formula: see text] for each [Formula: see text], where [Formula: see text] and [Formula: see text]. In this note, the graph with the minimal least eigenvalue (and the graph with maximal spread) in [Formula: see text] is determined.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91064738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000177
A. Alahmadi, Fawziah Alharthi
Let [Formula: see text] be a finitely generated associative algebra over a field of characteristic different from 2. Herstein asked when the Lie algebra [Formula: see text] is finitely generated. Recently, it was shown that for a finitely generated nil algebra [Formula: see text] all derived powers of [Formula: see text] are finitely generated Lie algebras. Let [Formula: see text] be the Lie algebra of skew-symmetric elements of an associative algebra with involution. We consider all derived powers of the Lie algebra [Formula: see text] and prove that for any finitely generated associative nil algebra with an involution, all derived powers of [Formula: see text] are finitely generated Lie algebras.
{"title":"Finite Generation of Lie Derived Powers of Skew Lie Algebras","authors":"A. Alahmadi, Fawziah Alharthi","doi":"10.1142/s1005386722000177","DOIUrl":"https://doi.org/10.1142/s1005386722000177","url":null,"abstract":"Let [Formula: see text] be a finitely generated associative algebra over a field of characteristic different from 2. Herstein asked when the Lie algebra [Formula: see text] is finitely generated. Recently, it was shown that for a finitely generated nil algebra [Formula: see text] all derived powers of [Formula: see text] are finitely generated Lie algebras. Let [Formula: see text] be the Lie algebra of skew-symmetric elements of an associative algebra with involution. We consider all derived powers of the Lie algebra [Formula: see text] and prove that for any finitely generated associative nil algebra with an involution, all derived powers of [Formula: see text] are finitely generated Lie algebras.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78996368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000232
R. Raja, S. Pirzada
Let [Formula: see text] be a commutative ring with unity, [Formula: see text] be a unitary [Formula: see text]-module and [Formula: see text] be a simple connected graph. We examine different equivalence relations on subsets [Formula: see text], [Formula: see text] and [Formula: see text] of [Formula: see text], where [Formula: see text] is the set of full-annihilators, [Formula: see text] is the set of semi-annihilators and [Formula: see text] is the set of star-annihilators in [Formula: see text]. We prove that elements [Formula: see text] are neighborhood similar in the annihilating graph [Formula: see text] if and only if the submodules [Formula: see text] and [Formula: see text] of [Formula: see text] are equal. We study the isomorphism of annihilating graphs arising from [Formula: see text] and the tensor product [Formula: see text], where [Formula: see text], [Formula: see text].
{"title":"On Annihilating Graphs Associated with Modules over Commutative Rings","authors":"R. Raja, S. Pirzada","doi":"10.1142/s1005386722000232","DOIUrl":"https://doi.org/10.1142/s1005386722000232","url":null,"abstract":"Let [Formula: see text] be a commutative ring with unity, [Formula: see text] be a unitary [Formula: see text]-module and [Formula: see text] be a simple connected graph. We examine different equivalence relations on subsets [Formula: see text], [Formula: see text] and [Formula: see text] of [Formula: see text], where [Formula: see text] is the set of full-annihilators, [Formula: see text] is the set of semi-annihilators and [Formula: see text] is the set of star-annihilators in [Formula: see text]. We prove that elements [Formula: see text] are neighborhood similar in the annihilating graph [Formula: see text] if and only if the submodules [Formula: see text] and [Formula: see text] of [Formula: see text] are equal. We study the isomorphism of annihilating graphs arising from [Formula: see text] and the tensor product [Formula: see text], where [Formula: see text], [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87836322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000153
Ayman Badawi, Ece Yetkin Çelikel
Let [Formula: see text] be a commutative ring with [Formula: see text]. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal [Formula: see text] of [Formula: see text] is said to be weakly 1-absorbing primary if whenever nonunit elements [Formula: see text] and [Formula: see text], we have [Formula: see text] or [Formula: see text]. A number of results concerning weakly 1-absorbing primary ideals are given, as well as examples of weakly 1-absorbing primary ideals. Furthermore, we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.
{"title":"On Weakly 1-Absorbing Primary Ideals of Commutative Rings","authors":"Ayman Badawi, Ece Yetkin Çelikel","doi":"10.1142/s1005386722000153","DOIUrl":"https://doi.org/10.1142/s1005386722000153","url":null,"abstract":"Let [Formula: see text] be a commutative ring with [Formula: see text]. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal [Formula: see text] of [Formula: see text] is said to be weakly 1-absorbing primary if whenever nonunit elements [Formula: see text] and [Formula: see text], we have [Formula: see text] or [Formula: see text]. A number of results concerning weakly 1-absorbing primary ideals are given, as well as examples of weakly 1-absorbing primary ideals. Furthermore, we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82026684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.1142/s1005386722000190
Berke Kalebog̃az, D. Keskin Tütüncü
Let 𝒜 be an abelian category and [Formula: see text]. Then M is called a [Formula: see text]-object if, whenever A and B are subobjects of M with [Formula: see text] and [Formula: see text] is an epimorphism, [Formula: see text] is a direct summand of A. In this paper we give several equivalent conditions of [Formula: see text]-objects in an abelian category. Among other results, we prove that any object M in an abelian category 𝒜 is [Formula: see text] if and only if for every subobject K of M such that K is the intersection [Formula: see text] of perspective direct summands [Formula: see text] and [Formula: see text] of M with [Formula: see text], every morphismr [Formula: see text] can be lifted to an endomorphism [Formula: see text] in [Formula: see text].
{"title":"(D4)-Objects in Abelian Categories","authors":"Berke Kalebog̃az, D. Keskin Tütüncü","doi":"10.1142/s1005386722000190","DOIUrl":"https://doi.org/10.1142/s1005386722000190","url":null,"abstract":"Let 𝒜 be an abelian category and [Formula: see text]. Then M is called a [Formula: see text]-object if, whenever A and B are subobjects of M with [Formula: see text] and [Formula: see text] is an epimorphism, [Formula: see text] is a direct summand of A. In this paper we give several equivalent conditions of [Formula: see text]-objects in an abelian category. Among other results, we prove that any object M in an abelian category 𝒜 is [Formula: see text] if and only if for every subobject K of M such that K is the intersection [Formula: see text] of perspective direct summands [Formula: see text] and [Formula: see text] of M with [Formula: see text], every morphismr [Formula: see text] can be lifted to an endomorphism [Formula: see text] in [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87123555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-20DOI: 10.1142/s1005386723000123
J. Liao, H. Liu, Xiaoliang Luo, Xingzhong Xu
Let [Formula: see text] be a completely decomposable homogeneous torsion-free abelian group of rank [Formula: see text] ([Formula: see text]). Let [Formula: see text] be the split extension of [Formula: see text] by an automorphism [Formula: see text] which is a cyclic permutation of the direct components twisted by a rational integer [Formula: see text]. Then [Formula: see text] is an infinite soluble group. In this paper, the residual finiteness of [Formula: see text] is investigated.
{"title":"On the Residual Finiteness of a Class of Infinite Soluble Groups","authors":"J. Liao, H. Liu, Xiaoliang Luo, Xingzhong Xu","doi":"10.1142/s1005386723000123","DOIUrl":"https://doi.org/10.1142/s1005386723000123","url":null,"abstract":"Let [Formula: see text] be a completely decomposable homogeneous torsion-free abelian group of rank [Formula: see text] ([Formula: see text]). Let [Formula: see text] be the split extension of [Formula: see text] by an automorphism [Formula: see text] which is a cyclic permutation of the direct components twisted by a rational integer [Formula: see text]. Then [Formula: see text] is an infinite soluble group. In this paper, the residual finiteness of [Formula: see text] is investigated.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74294175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-20DOI: 10.1142/s1005386723000093
K. Cheng
Let [Formula: see text] be an odd prime, and [Formula: see text], [Formula: see text] be nonnegative integers. Let [Formula: see text] be the reversed Dickson polynomial of the [Formula: see text]-th kind. In this paper, by using Hermite's criterion, we study the permutational properties of the reversed Dickson polynomials [Formula: see text] over finite fields in the case of [Formula: see text] with [Formula: see text]. In particular, we provide some precise characterizations for [Formula: see text] being permutation polynomials over finite fields with characteristic [Formula: see text] when [Formula: see text], or [Formula: see text], or [Formula: see text].
{"title":"New Permutation Reversed Dickson Polynomials over Finite Fields","authors":"K. Cheng","doi":"10.1142/s1005386723000093","DOIUrl":"https://doi.org/10.1142/s1005386723000093","url":null,"abstract":"Let [Formula: see text] be an odd prime, and [Formula: see text], [Formula: see text] be nonnegative integers. Let [Formula: see text] be the reversed Dickson polynomial of the [Formula: see text]-th kind. In this paper, by using Hermite's criterion, we study the permutational properties of the reversed Dickson polynomials [Formula: see text] over finite fields in the case of [Formula: see text] with [Formula: see text]. In particular, we provide some precise characterizations for [Formula: see text] being permutation polynomials over finite fields with characteristic [Formula: see text] when [Formula: see text], or [Formula: see text], or [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73251264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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