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Asian-European Journal of Mathematics最新文献

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On Graded (1,r)-Ideals 关于分级(1,r)-理想
Asian-European Journal of Mathematics Pub Date : 2023-11-07 DOI: 10.1142/s1793557123502224
Nassima Guennach, Najib Mahdou, Unsal Tekir, Suat Koc
{"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":null,"pages":null},"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}
引用次数: 0
Pseudo-prime submodule elements of an le-module 一个le-module的伪素数子模块元素
Asian-European Journal of Mathematics Pub Date : 2023-11-04 DOI: 10.1142/s1793557123502248
M. Kumbhakar, A. K. Bhuniya
{"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":null,"pages":null},"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}
引用次数: 1
Pure C3 Modules 纯C3模块
Asian-European Journal of Mathematics Pub Date : 2023-10-27 DOI: 10.1142/s1793557123502194
Kaushal Gupta, Ashok Ji Gupta
{"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":null,"pages":null},"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}
引用次数: 0
Finite Direct Projective modules 有限直射影模
Asian-European Journal of Mathematics Pub Date : 2023-10-27 DOI: 10.1142/s1793557123502182
Sonal Gupta, Ashok Ji Gupta
{"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":null,"pages":null},"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}
引用次数: 0
Product of Generalized Derivations with Engel Condition on Lie ideals in prime rings 素环上Lie理想上具有Engel条件的广义导数的积
Asian-European Journal of Mathematics Pub Date : 2023-10-27 DOI: 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":null,"pages":null},"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}
引用次数: 0
On weak-like comultiplication modules 在类弱乘法模块上
Asian-European Journal of Mathematics Pub Date : 2023-10-27 DOI: 10.1142/s1793557123502327
Fatemeh Rashedi
{"title":"On weak-like comultiplication modules","authors":"Fatemeh Rashedi","doi":"10.1142/s1793557123502327","DOIUrl":"https://doi.org/10.1142/s1793557123502327","url":null,"abstract":"","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312447","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}
引用次数: 0
On the asymptotic stabilization of the non-autonomous evolution equations in Hilbert spaces Hilbert空间中非自治演化方程的渐近镇定
Asian-European Journal of Mathematics Pub Date : 2023-10-21 DOI: 10.1142/s1793557123502212
Hanen Damak, Mohamed Ali Hammami, Khouloud Maaloul
{"title":"On the asymptotic stabilization of the non-autonomous evolution equations in Hilbert spaces","authors":"Hanen Damak, Mohamed Ali Hammami, Khouloud Maaloul","doi":"10.1142/s1793557123502212","DOIUrl":"https://doi.org/10.1142/s1793557123502212","url":null,"abstract":"This paper deals with the practical feedback stabilization of a class of evolution equations in Hilbert spaces. By using the Lyapunov function method, we give sufficient conditions for the global uniform practical convergence of the closed-loop system. Based on the global null-controllability, we construct an output feedback controller that guarantees global uniform practical stability of uncertain systems. A numerical application is given to show the applicability of our theoretical results.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135463228","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}
引用次数: 0
On the semisimplicity of twisted group rings and generalized maschke's theorem 关于扭群环的半简单性和广义maschke定理
Asian-European Journal of Mathematics Pub Date : 2023-10-21 DOI: 10.1142/s1793557123502200
Alanka Thomas, P.G. Romeo
{"title":"On the semisimplicity of twisted group rings and generalized maschke's theorem","authors":"Alanka Thomas, P.G. Romeo","doi":"10.1142/s1793557123502200","DOIUrl":"https://doi.org/10.1142/s1793557123502200","url":null,"abstract":"Classical Maschke’s theorem gives a condition for the semisimplicity of group algebras over a field. As group algebras are a particular case of twisted group rings, we extend Maschke’s theorem to twisted group rings over division rings by proving that if the characteristic of a division ring [Formula: see text] does not divide the order of a finite group [Formula: see text], twisted group ring [Formula: see text] is semisimple. Then we prove the converse of this theorem for twisted group rings arising from split extensions of [Formula: see text] by [Formula: see text]. As there is a one-to-one correspondence between twisted group rings and group lattices over division rings, we conclude with the consequence of the semisimplicity of twisted group rings on group lattices.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135463226","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}
引用次数: 0
Commutativity with algebraic identities involving hermetian and skew-hermetian elements 代数恒等式的交换性，包括荷密和斜荷密元素
Asian-European Journal of Mathematics Pub Date : 2023-10-20 DOI: 10.1142/s1793557123502145
H. Aharssi, H. El Mir, A. Mamouni
{"title":"Commutativity with algebraic identities involving hermetian and skew-hermetian elements","authors":"H. Aharssi, H. El Mir, A. Mamouni","doi":"10.1142/s1793557123502145","DOIUrl":"https://doi.org/10.1142/s1793557123502145","url":null,"abstract":"This paper aims to investigate the commutativity of prime rings with involution ∗ of the second kind in which endomorphisms satisfy some algebraic identities involving hermitian and skew-hermitian elements. We will also provide some classifications of these endomorphisms. Finally, we give some examples to prove that the imposed hypotheses are necessary.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514410","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}
引用次数: 0
Some inequalities for convex functions and applications to operator inequalities 凸函数的若干不等式及其在算子不等式上的应用
Asian-European Journal of Mathematics Pub Date : 2023-10-20 DOI: 10.1142/s1793557123502169
Duong Quoc Huy, Doan Thi Thuy Van
{"title":"Some inequalities for convex functions and applications to operator inequalities","authors":"Duong Quoc Huy, Doan Thi Thuy Van","doi":"10.1142/s1793557123502169","DOIUrl":"https://doi.org/10.1142/s1793557123502169","url":null,"abstract":"In this paper we propose some Heinz-type inequalities for convex functions which provide a very simple proof of the main results of Kittaneh, Moslehian and Sababheh showed in the paper (F. Kittaneh, M. S. Moslehian and M. Sababheh, Quadratic interpolation of the Heinz means, Math. Inequal. Appl. 21(3) (2018) 739–757). We apply these inequalities to infer new inequalities for power means. As an application, we also give operator versions of Heinz-type inequalities for power and Heinz means.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514279","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}
引用次数: 0
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