{"title":"The socle of Leavitt path algebras over a semiprime ring","authors":"K. Wardati","doi":"10.12958/adm1850","DOIUrl":"https://doi.org/10.12958/adm1850","url":null,"abstract":"The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path algebra. Vice versa, any left minimal ideal in the semiprime Leavitt path algebra can be found both minimal ideal in the semiprime ring and line point that generate it. The socle of semiprime Leavitt path algebra is constructed by minimal ideals of the semiprime ring and the set of all line points.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420239","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}
{"title":"On cofinitely ss-supplemented modules","authors":"B. Türkmen, B. Kılıç","doi":"10.12958/adm1668","DOIUrl":"https://doi.org/10.12958/adm1668","url":null,"abstract":"In this paper, we introduce the concept of (amply) cofinitely ss-supplemented modules as a proper generalization of (amply) ss-supplemented modules, and we provide various properties of these modules. In particular, we prove that arbitrary sum of cofinitely ss-supplemented modules is cofinitely ss-supplemented. Moreover, we show that a ring R is semiperfect and Rad(R)⊆Soc(RR) if and only if every left R-module (amply) cofinitely ss-supplemented.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419387","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}
{"title":"Binary matroids that classify forests","authors":"L. Traldi","doi":"10.12958/adm1759","DOIUrl":"https://doi.org/10.12958/adm1759","url":null,"abstract":"Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419739","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}
Abderrahim El Moussaouy, A. R. Moniri Hamzekolaee, M. Ziane
{"title":"Jacobson Hopfian modules","authors":"Abderrahim El Moussaouy, A. R. Moniri Hamzekolaee, M. Ziane","doi":"10.12958/adm1842","DOIUrl":"https://doi.org/10.12958/adm1842","url":null,"abstract":"The study of modules by properties of their endomorphisms has long been of interest. In this paper we introduce a proper generalization of that of Hopfian modules, called Jacobson Hopfian modules. A right R-module M is said to be Jacobson Hopfian, if any surjective endomorphism of M has a Jacobson-small kernel. We characterize the rings R for which every finitely generated free R-module is Jacobson Hopfian. We prove that a ring R is semisimple if and only if every R-module is Jacobson Hopfian. Some other properties and characterizations of Jacobson Hopfian modules are also obtained with examples. Further, we prove that the Jacobson Hopfian property is preserved under Morita equivalences.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420039","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}
{"title":"Central and non central codes of dihedral 2-groups","authors":"Shalini Gupta, P. Rani","doi":"10.12958/adm1569","DOIUrl":"https://doi.org/10.12958/adm1569","url":null,"abstract":"In this paper, the central and non central codesof semisimple dihedral group algebra FqG, over a finite field Fq, are constructed. Further the distances of these central and non central codes are computed.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66418528","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}
{"title":"A note on modular group algebras with upper Lie nilpotency indices","authors":"Suchi Bhatt, H. Chandra","doi":"10.12958/adm1694","DOIUrl":"https://doi.org/10.12958/adm1694","url":null,"abstract":"Let KG be the modular group algebra of anarbitrary group G over a field K of characteristic p>0. In thispaper we give some improvements of upper Lie nilpotency indext L(KG) of the group algebra KG. It can be seen that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is atleast p+1. In this way the classification of group algebras KG with next upper Lie nilpotency indext L(KG) up to 9p−7 have alreadybeen classified. Furthermore, we give a complete classification ofmodular group algebraKGfor which the upper Lie nilpotency index is 10p−8.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419441","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}
{"title":"Groupoids: Direct products, semidirect products and solvability","authors":"Víctor Marín, H. Pinedo","doi":"10.12958/adm1772","DOIUrl":"https://doi.org/10.12958/adm1772","url":null,"abstract":"We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid G is solvable if and only if its isotropy groups are.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419595","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}
{"title":"On special subalgebras of derivations of Leibniz algebras","authors":"Z. Shermatova, A. Khudoyberdiyev","doi":"10.12958/adm1895","DOIUrl":"https://doi.org/10.12958/adm1895","url":null,"abstract":"Our aim in this work is to study the central derivations of Leibniz algebras and investigate the properties of Leibniz algebras by comparing the set of central derivations with the inner derivations. We prove that, the set of all central derivations of a Leibniz algebra with non-trivial center coincide with the set of all inner derivations if and only if the Leibniz algebra is metabelian. In addition, we will show, by examples, that some statements hold for arbitrary Lie algebras, but does not hold for some Leibniz algebras.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420056","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}
{"title":"Double-toroidal and 1-planar non-commuting graph of a group","authors":"J. C. M. Pezzott","doi":"10.12958/adm1935","DOIUrl":"https://doi.org/10.12958/adm1935","url":null,"abstract":"Let G be a finite non-abelian group and denote by Z(G) its center. The non-commuting graph of G on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of Z(G) in G and two vertices x and y are adjacent whenever xy=yx. In this work, we classify the finite non-abelian groups whose non-commuting graph on a transversal of the centeris double-toroidal or 1-planar.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420744","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}
{"title":"On products of 3-paths in finite full transformation semigroups","authors":"A. Imam, M. J. Ibrahim","doi":"10.12958/adm1770","DOIUrl":"https://doi.org/10.12958/adm1770","url":null,"abstract":"Let Singn denotes the semigroup of all singular self-maps of a finite set Xn={1,2, . . . , n}. A map α∈Singn is called a 3-path if there are i, j, k∈Xn such that iα=j,jα=k and xα=x for all x∈Xn {i, j}. In this paper, we described aprocedure to factorise each α∈Singn into a product of 3-paths. The length of each factorisation, that is the number of factors in eachfactorisation, is obtained to be equal to ⌈12(g(α)+m(α))⌉, where g(α) is known as the gravity of α and m(α) is a parameter introduced inthis work and referred to as the measure of α. Moreover, we showed that Singn⊆P[n−1], where P denotes the set of all 3-paths in Singn and P[k]=P∪P2∪ ··· ∪Pk.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419588","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
