Pub Date : 2023-11-16DOI: 10.1142/s1793557123502340
M. Mahmoudi, Alireza Mehdizadeh
{"title":"Baer criterion for injectivity in abelian categories","authors":"M. Mahmoudi, Alireza Mehdizadeh","doi":"10.1142/s1793557123502340","DOIUrl":"https://doi.org/10.1142/s1793557123502340","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139268575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-15DOI: 10.1142/s1793557123502315
Mehmet Ali Ozturk
The purpose of this paper is to describe the nearness homomorphisms and the canonical nearness epimorphism of the nearness groups and to investigate their basic properties. It is also to form the substructure to give the nearness isomorphism theorems of the nearness groups.
{"title":"Nearness isomorphisms of the nearness groups","authors":"Mehmet Ali Ozturk","doi":"10.1142/s1793557123502315","DOIUrl":"https://doi.org/10.1142/s1793557123502315","url":null,"abstract":"The purpose of this paper is to describe the nearness homomorphisms and the canonical nearness epimorphism of the nearness groups and to investigate their basic properties. It is also to form the substructure to give the nearness isomorphism theorems of the nearness groups.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"14 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136226837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1142/s1793557123502236
Apatsara Sareeto, Jorg Koppitz
The monoid of all partial injections on a finite set (the symmetric inverse semigroup) is of particular interest because of the well-known Wagner–Preston Theorem. Let [Formula: see text] be a positive natural number and [Formula: see text] be the semigroup of all fence-preserving partial one-to-one maps of [Formula: see text] into itself with respect to composition of maps and the fence [Formula: see text]. There is considered the inverse semigroup [Formula: see text] of all [Formula: see text] such that [Formula: see text] is regular in [Formula: see text], order-preserving with respect to the order [Formula: see text] and parity-preserving. According to the main result of the paper, it is [Formula: see text] the least of the cardinalities of the generating sets of [Formula: see text] for [Formula: see text]. There is determined a concrete representation of a generating set of minimal size.
{"title":"The rank of the semigroup of order-, fence-, and parity-preserving partial injections on a finite set","authors":"Apatsara Sareeto, Jorg Koppitz","doi":"10.1142/s1793557123502236","DOIUrl":"https://doi.org/10.1142/s1793557123502236","url":null,"abstract":"The monoid of all partial injections on a finite set (the symmetric inverse semigroup) is of particular interest because of the well-known Wagner–Preston Theorem. Let [Formula: see text] be a positive natural number and [Formula: see text] be the semigroup of all fence-preserving partial one-to-one maps of [Formula: see text] into itself with respect to composition of maps and the fence [Formula: see text]. There is considered the inverse semigroup [Formula: see text] of all [Formula: see text] such that [Formula: see text] is regular in [Formula: see text], order-preserving with respect to the order [Formula: see text] and parity-preserving. According to the main result of the paper, it is [Formula: see text] the least of the cardinalities of the generating sets of [Formula: see text] for [Formula: see text]. There is determined a concrete representation of a generating set of minimal size.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"74 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1142/s1793557123502303
Mykola Yaremenko
In this paper, we are establishing the generalized variant of the Hardy theorem, which states that for [Formula: see text] a separable Hilbert space, [Formula: see text] a connected semi-simple Lie group with a Haar measure [Formula: see text] a unitary representation of [Formula: see text] in [Formula: see text], and [Formula: see text] a dual measure on [Formula: see text], if inequalities [Formula: see text] and [Formula: see text] hold for [Formula: see text], then the function [Formula: see text] must equal zero almost for all [Formula: see text].
{"title":"The uncertainty principle generalization for a connected semi-simple Lie group","authors":"Mykola Yaremenko","doi":"10.1142/s1793557123502303","DOIUrl":"https://doi.org/10.1142/s1793557123502303","url":null,"abstract":"In this paper, we are establishing the generalized variant of the Hardy theorem, which states that for [Formula: see text] a separable Hilbert space, [Formula: see text] a connected semi-simple Lie group with a Haar measure [Formula: see text] a unitary representation of [Formula: see text] in [Formula: see text], and [Formula: see text] a dual measure on [Formula: see text], if inequalities [Formula: see text] and [Formula: see text] hold for [Formula: see text], then the function [Formula: see text] must equal zero almost for all [Formula: see text].","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"73 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1142/s1793557123502273
Sushree Khirabdhi, Shubh N. Singh
Let [Formula: see text] be the full transformation semigroup on a set [Formula: see text]. For a subset [Formula: see text] of [Formula: see text] and a submonoid [Formula: see text] of [Formula: see text], denote by [Formula: see text] the semigroup under composition consisting of all transformations [Formula: see text] such that the restriction [Formula: see text] of [Formula: see text] to [Formula: see text] belongs to [Formula: see text]. We give necessary and sufficient conditions for an element in [Formula: see text] to be left or right magnifier. We apply these descriptions to obtain more concrete results for the semigroups [Formula: see text] and [Formula: see text], where [Formula: see text] (respectively, [Formula: see text]) is the specific submonoid of [Formula: see text] consisting of all injective (respectively, surjective) transformations. The paper also identifies some results on [Formula: see text] that have appeared in the literature.
{"title":"Magnifiers in semigroups of transformations whose restrictions belong to a given semigroup","authors":"Sushree Khirabdhi, Shubh N. Singh","doi":"10.1142/s1793557123502273","DOIUrl":"https://doi.org/10.1142/s1793557123502273","url":null,"abstract":"Let [Formula: see text] be the full transformation semigroup on a set [Formula: see text]. For a subset [Formula: see text] of [Formula: see text] and a submonoid [Formula: see text] of [Formula: see text], denote by [Formula: see text] the semigroup under composition consisting of all transformations [Formula: see text] such that the restriction [Formula: see text] of [Formula: see text] to [Formula: see text] belongs to [Formula: see text]. We give necessary and sufficient conditions for an element in [Formula: see text] to be left or right magnifier. We apply these descriptions to obtain more concrete results for the semigroups [Formula: see text] and [Formula: see text], where [Formula: see text] (respectively, [Formula: see text]) is the specific submonoid of [Formula: see text] consisting of all injective (respectively, surjective) transformations. The paper also identifies some results on [Formula: see text] that have appeared in the literature.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":" 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let [Formula: see text] be a group with identity element [Formula: see text] and [Formula: see text] be a commutative [Formula: see text]-graded ring with nonzero unity [Formula: see text]. In this paper, we introduce the graded version of [Formula: see text]-ideals which is a generalization of graded [Formula: see text]-ideals. A proper graded ideal [Formula: see text] of [Formula: see text] is said to be a graded [Formula: see text]-ideal if whenever [Formula: see text] for some nonunits homogeneous elements [Formula: see text], then either [Formula: see text] or [Formula: see text]. We investigate some basic properties of graded [Formula: see text]-ideals. We show that if [Formula: see text] admits a graded [Formula: see text]-ideal that is not a graded [Formula: see text]-ideal, then [Formula: see text] is a [Formula: see text]-graded local ring. Also, we give a method to construct graded [Formula: see text]-ideals that are not graded [Formula: see text]-ideals. Furthermore, we prove that [Formula: see text] is a graded total quotient ring if and only if every proper graded ideal of [Formula: see text] is graded [Formula: see text]-ideal and also we present a counterpart of prime avoidance lemma for graded [Formula: see text]-ideals. Finally, an idea is given about some graded [Formula: see text]-ideals of the ring of fractions and the idealization.
{"title":"On Graded (1,<i>r</i>)-Ideals","authors":"Nassima Guennach, Najib Mahdou, Unsal Tekir, Suat Koc","doi":"10.1142/s1793557123502224","DOIUrl":"https://doi.org/10.1142/s1793557123502224","url":null,"abstract":"Let [Formula: see text] be a group with identity element [Formula: see text] and [Formula: see text] be a commutative [Formula: see text]-graded ring with nonzero unity [Formula: see text]. In this paper, we introduce the graded version of [Formula: see text]-ideals which is a generalization of graded [Formula: see text]-ideals. A proper graded ideal [Formula: see text] of [Formula: see text] is said to be a graded [Formula: see text]-ideal if whenever [Formula: see text] for some nonunits homogeneous elements [Formula: see text], then either [Formula: see text] or [Formula: see text]. We investigate some basic properties of graded [Formula: see text]-ideals. We show that if [Formula: see text] admits a graded [Formula: see text]-ideal that is not a graded [Formula: see text]-ideal, then [Formula: see text] is a [Formula: see text]-graded local ring. Also, we give a method to construct graded [Formula: see text]-ideals that are not graded [Formula: see text]-ideals. Furthermore, we prove that [Formula: see text] is a graded total quotient ring if and only if every proper graded ideal of [Formula: see text] is graded [Formula: see text]-ideal and also we present a counterpart of prime avoidance lemma for graded [Formula: see text]-ideals. Finally, an idea is given about some graded [Formula: see text]-ideals of the ring of fractions and the idealization.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"20 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-04DOI: 10.1142/s1793557123502248
M. Kumbhakar, A. K. Bhuniya
Here we introduce and study the concept of pseudo-prime submodule elements of an le-module. The pseudo-prime submodule elements of an le-module are useful to characterize several class, like topological, multiplication, content, pseudo-primeful le-modules. Besides we extend the Nakayama’s lemma to le-modules.
{"title":"Pseudo-prime submodule elements of an le-module","authors":"M. Kumbhakar, A. K. Bhuniya","doi":"10.1142/s1793557123502248","DOIUrl":"https://doi.org/10.1142/s1793557123502248","url":null,"abstract":"Here we introduce and study the concept of pseudo-prime submodule elements of an le-module. The pseudo-prime submodule elements of an le-module are useful to characterize several class, like topological, multiplication, content, pseudo-primeful le-modules. Besides we extend the Nakayama’s lemma to le-modules.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"13 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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/s1793557123502194
Kaushal Gupta, Ashok Ji Gupta
Within the paper, we study the class of modules in which the direct sum of two disjoint summands that is a pure submodule is also a summand. This class of modules is considered [Formula: see text] modules, a generalization of [Formula: see text] modules. In addition to pure-injective and [Formula: see text] modules that belong to the class of [Formula: see text] modules, which also include the semisimple, continuous, indecomposable, and regular modules. We gave new characterizations of many rings in respect of [Formula: see text] modules, namely semisimple rings, pure-semisimple rings, von Neumann regular rings, Noetherian rings, pure-hereditary rings, pure-[Formula: see text]-rings, etc. Moreover, we also discuss the [Formula: see text] envelope and [Formula: see text] cover of a module and introduce the pure continuous modules as the generalization of the continuous modules and also introduce the pure quasi-continuous modules as the generalization of the quasi-continuous modules.
{"title":"Pure C3 Modules","authors":"Kaushal Gupta, Ashok Ji Gupta","doi":"10.1142/s1793557123502194","DOIUrl":"https://doi.org/10.1142/s1793557123502194","url":null,"abstract":"Within the paper, we study the class of modules in which the direct sum of two disjoint summands that is a pure submodule is also a summand. This class of modules is considered [Formula: see text] modules, a generalization of [Formula: see text] modules. In addition to pure-injective and [Formula: see text] modules that belong to the class of [Formula: see text] modules, which also include the semisimple, continuous, indecomposable, and regular modules. We gave new characterizations of many rings in respect of [Formula: see text] modules, namely semisimple rings, pure-semisimple rings, von Neumann regular rings, Noetherian rings, pure-hereditary rings, pure-[Formula: see text]-rings, etc. Moreover, we also discuss the [Formula: see text] envelope and [Formula: see text] cover of a module and introduce the pure continuous modules as the generalization of the continuous modules and also introduce the pure quasi-continuous modules as the generalization of the quasi-continuous modules.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"32 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":"136233030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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/s1793557123502182
Sonal Gupta, Ashok Ji Gupta
In this paper, we introduce the notion of finite direct projective modules, which is a generalization of direct projective modules; counter-example is given. We study the properties of finite direct projective modules with respect of their summands. We characterized von Neumann regular rings in terms of the endomorphism ring of finite direct projective modules. Also, we find connections among Rickart modules, [Formula: see text] modules, direct projective modules, finite direct projective modules and endoregular modules.
{"title":"Finite Direct Projective modules","authors":"Sonal Gupta, Ashok Ji Gupta","doi":"10.1142/s1793557123502182","DOIUrl":"https://doi.org/10.1142/s1793557123502182","url":null,"abstract":"In this paper, we introduce the notion of finite direct projective modules, which is a generalization of direct projective modules; counter-example is given. We study the properties of finite direct projective modules with respect of their summands. We characterized von Neumann regular rings in terms of the endomorphism ring of finite direct projective modules. Also, we find connections among Rickart modules, [Formula: see text] modules, direct projective modules, finite direct projective modules and endoregular modules.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"27 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":"136233029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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/s1793557123502339
Basudeb Dhara, Sukhendu Kar, Kalyan Singh
{"title":"Product of Generalized Derivations with Engel Condition on Lie ideals in prime rings","authors":"Basudeb Dhara, Sukhendu Kar, Kalyan Singh","doi":"10.1142/s1793557123502339","DOIUrl":"https://doi.org/10.1142/s1793557123502339","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":"49 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":"136312427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：