Pub Date : 2023-10-31DOI: 10.1142/s0219498825501300
M. Adlifard, Sh. Niknejad, R. Nikandish
The prime ideal sum graph of a commutative unital ring $R$, denoted by $PIS(R)$, is an undirect and simple graph whose vertices are non-trivial ideals of $R$ and there exists and edge between to distinct vertices if and only if their sum is a prime ideal of $R$. In this paper, the metric dimension of $PIS(R)$ is discussed and some formulae for this parameter in $PIS(R)$ are given.
{"title":"Metric dimension in a prime ideal sum graph of a commutative ring","authors":"M. Adlifard, Sh. Niknejad, R. Nikandish","doi":"10.1142/s0219498825501300","DOIUrl":"https://doi.org/10.1142/s0219498825501300","url":null,"abstract":"The prime ideal sum graph of a commutative unital ring $R$, denoted by $PIS(R)$, is an undirect and simple graph whose vertices are non-trivial ideals of $R$ and there exists and edge between to distinct vertices if and only if their sum is a prime ideal of $R$. In this paper, the metric dimension of $PIS(R)$ is discussed and some formulae for this parameter in $PIS(R)$ are given.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"34 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135863531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1142/s0219498825501324
Yi-Yang Li
{"title":"The Modular Representations of Basic Classical Restricted Lie Superalgebras","authors":"Yi-Yang Li","doi":"10.1142/s0219498825501324","DOIUrl":"https://doi.org/10.1142/s0219498825501324","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1142/s0219498825501270
Emily McMillon, Christine A. Kelley
{"title":"Window Code Parameters of Spatially-Coupled LDPC Codes","authors":"Emily McMillon, Christine A. Kelley","doi":"10.1142/s0219498825501270","DOIUrl":"https://doi.org/10.1142/s0219498825501270","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1142/s0219498825501282
Rabia Iqbal, Cuipo Jiang
{"title":"Fusion rules for the orbifold vertex operator algebras L𝔰𝔩2̂(k,0)K","authors":"Rabia Iqbal, Cuipo Jiang","doi":"10.1142/s0219498825501282","DOIUrl":"https://doi.org/10.1142/s0219498825501282","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135928796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-28DOI: 10.1142/s0219498825500811
Ping Zhao, Huabi Hu
Let [Formula: see text] be a non-empty set and let [Formula: see text] be the monoid of all full transformations of [Formula: see text]. Given a non-empty subset [Formula: see text] of [Formula: see text], we denote by [Formula: see text] the subsemigroup of [Formula: see text] of all full transformations with range contained in [Formula: see text] and by [Formula: see text] the monoid of all full transformations of [Formula: see text]. In 2011, Sanwong investigated the subsemigroup [Formula: see text] of [Formula: see text]. For [Formula: see text] is a finite set with [Formula: see text], put [Formula: see text] We characterize the connections between the maximal regular subsemigroups of ideals of [Formula: see text] and the maximal regular subsemigroups of ideals of [Formula: see text]. Moreover, we determine the maximal subsemigroups of [Formula: see text] and classify completely the maximal regular subsemigroups of the ideals [Formula: see text] of [Formula: see text], for [Formula: see text]. We also show that, for [Formula: see text], any maximal regular subsemigroup of [Formula: see text] is idempotent generated.
{"title":"The ideals of the monoid of all full transformations with restricted range","authors":"Ping Zhao, Huabi Hu","doi":"10.1142/s0219498825500811","DOIUrl":"https://doi.org/10.1142/s0219498825500811","url":null,"abstract":"Let [Formula: see text] be a non-empty set and let [Formula: see text] be the monoid of all full transformations of [Formula: see text]. Given a non-empty subset [Formula: see text] of [Formula: see text], we denote by [Formula: see text] the subsemigroup of [Formula: see text] of all full transformations with range contained in [Formula: see text] and by [Formula: see text] the monoid of all full transformations of [Formula: see text]. In 2011, Sanwong investigated the subsemigroup [Formula: see text] of [Formula: see text]. For [Formula: see text] is a finite set with [Formula: see text], put [Formula: see text] We characterize the connections between the maximal regular subsemigroups of ideals of [Formula: see text] and the maximal regular subsemigroups of ideals of [Formula: see text]. Moreover, we determine the maximal subsemigroups of [Formula: see text] and classify completely the maximal regular subsemigroups of the ideals [Formula: see text] of [Formula: see text], for [Formula: see text]. We also show that, for [Formula: see text], any maximal regular subsemigroup of [Formula: see text] is idempotent generated.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"4 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136157335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-28DOI: 10.1142/s0219498825500793
B. G. Rodrigues
Using an approach from finite group representation theory we construct quaternary non-projective codes with parameters [Formula: see text], quaternary projective codes with parameters [Formula: see text] and [Formula: see text] and binary projective codes with parameters [Formula: see text] as examples of two-weight codes on which a finite almost quasisimple group of sporadic type acts transitively as permutation groups of automorphisms. In particular, we show that these codes are invariant under the [Formula: see text]-fold covers [Formula: see text] and [Formula: see text], respectively, of the Mathieu groups [Formula: see text] and [Formula: see text]. Employing a known construction of strongly regular graphs from projective two-weight codes we obtain from the binary projective (respectively, quaternary projective) two-weight codes with parameters those given above, the strongly regular graphs with parameters [Formula: see text] and [Formula: see text] respectively. The latter graph can be viewed as a [Formula: see text]-[Formula: see text]-symmetric design with the symmetric difference property whose residual and derived designs with respect to a block give rise to binary self-complementary codes meeting the Grey–Rankin bound with equality.
{"title":"Some Two-Weight Codes Invariant Under the 3-fold covers of the Mathieu groups M<sub>22</sub> and Aut(M<sub>22</sub>)","authors":"B. G. Rodrigues","doi":"10.1142/s0219498825500793","DOIUrl":"https://doi.org/10.1142/s0219498825500793","url":null,"abstract":"Using an approach from finite group representation theory we construct quaternary non-projective codes with parameters [Formula: see text], quaternary projective codes with parameters [Formula: see text] and [Formula: see text] and binary projective codes with parameters [Formula: see text] as examples of two-weight codes on which a finite almost quasisimple group of sporadic type acts transitively as permutation groups of automorphisms. In particular, we show that these codes are invariant under the [Formula: see text]-fold covers [Formula: see text] and [Formula: see text], respectively, of the Mathieu groups [Formula: see text] and [Formula: see text]. Employing a known construction of strongly regular graphs from projective two-weight codes we obtain from the binary projective (respectively, quaternary projective) two-weight codes with parameters those given above, the strongly regular graphs with parameters [Formula: see text] and [Formula: see text] respectively. The latter graph can be viewed as a [Formula: see text]-[Formula: see text]-symmetric design with the symmetric difference property whose residual and derived designs with respect to a block give rise to binary self-complementary codes meeting the Grey–Rankin bound with equality.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"58 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136157318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-28DOI: 10.1142/s0219498825500847
Yaguo Guo, Shilin Yang
In this paper, representations of the [Formula: see text]-dimensional non-pointed Hopf algebra [Formula: see text] of tame type are studied, where [Formula: see text] is even. First, the isomorphism classes of all indecomposable modules of [Formula: see text] are classified and the components of Auslander–Reiten quivers are constructed. Second, the tensor products of arbitrary indecomposable modules and simple (or projective) modules are established and the projective class rings and Grothendieck rings of [Formula: see text] are characterized.
{"title":"Representations of an 8<i>m</i>-dimensional non-pointed Hopf algebra of tame type","authors":"Yaguo Guo, Shilin Yang","doi":"10.1142/s0219498825500847","DOIUrl":"https://doi.org/10.1142/s0219498825500847","url":null,"abstract":"In this paper, representations of the [Formula: see text]-dimensional non-pointed Hopf algebra [Formula: see text] of tame type are studied, where [Formula: see text] is even. First, the isomorphism classes of all indecomposable modules of [Formula: see text] are classified and the components of Auslander–Reiten quivers are constructed. Second, the tensor products of arbitrary indecomposable modules and simple (or projective) modules are established and the projective class rings and Grothendieck rings of [Formula: see text] are characterized.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"228 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136157336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1142/s021949882550121x
H. R. Dorbidi
{"title":"The diameter of commuting graph of matrix ring of division rings","authors":"H. R. Dorbidi","doi":"10.1142/s021949882550121x","DOIUrl":"https://doi.org/10.1142/s021949882550121x","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"4 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1142/s0219498825501245
Sarjick Bakshi
Let $k$ and $n$ be positive coprime integers with $k
{"title":"Smooth torus quotients of Richardson varieties in the Grassmannian","authors":"Sarjick Bakshi","doi":"10.1142/s0219498825501245","DOIUrl":"https://doi.org/10.1142/s0219498825501245","url":null,"abstract":"Let $k$ and $n$ be positive coprime integers with $k<n$. Let $T$ denote the subgroup of diagonal matrices in $SL(n,mathbb{C})$. We study the GIT quotient of Richardson varieties $X^v_w$ in the Grassmannian $mathrm{Gr}_{k,n}$ by $T$ with respect to a $T$-linearised line bundle $cal{L}$ corresponding to the Pl\"{u}cker embedding. We give necessary and sufficient combinatorial conditions for the quotient variety $T backslashmkern-6mubackslash (X_w^v)^{ss}_T({cal L})$ to be smooth.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1142/s0219498825501257
Sophie Marques, Daniella Moore
{"title":"Near-linear algebra","authors":"Sophie Marques, Daniella Moore","doi":"10.1142/s0219498825501257","DOIUrl":"https://doi.org/10.1142/s0219498825501257","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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