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On certain semigroups of contraction mappings of a finite chain 有限链的收缩映射的某些半群
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1816
A. Umar, M. M. Zubairu
{"title":"On certain semigroups of contraction mappings of a finite chain","authors":"A. Umar, M. M. Zubairu","doi":"10.12958/adm1816","DOIUrl":"https://doi.org/10.12958/adm1816","url":null,"abstract":"Let[n] ={1,2, . . . , n} be a finite chain and let Pn (resp.,Tn) be the semigroup of partial transformations on[n] (resp., full transformations on[n]). Let CPn={α∈ Pn: (for allx, y ∈ Dom α)|xα−yα|⩽|x−y|}(resp., CTn={α∈ Tn: (for allx, y∈[n])|xα−yα|⩽|x−y|}) be the subsemigroup of partial contractionmappings on[n](resp., subsemigroup of full contraction mappingson[n]). We characterize all the starred Green’s relations on C Pn and it subsemigroup of order preserving and/or order reversingand subsemigroup of order preserving partial contractions on[n], respectively. We show that the semigroups CPn and CTn, and some of their subsemigroups are left abundant semigroups for all n but not right abundant forn⩾4. We further show that the set ofregular elements of the semigroup CTn and its subsemigroup of order preserving or order reversing full contractions on[n], each formsa regular subsemigroup and an orthodox semigroup, respectively.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420014","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: 4
On the nilpotence of the prime radical in module categories 论模范畴中素根的幂零性
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1634
C. Arellano, J. Castro, J. Ríos
{"title":"On the nilpotence of the prime radical in module categories","authors":"C. Arellano, J. Castro, J. Ríos","doi":"10.12958/adm1634","DOIUrl":"https://doi.org/10.12958/adm1634","url":null,"abstract":"For M∈R-Mod and τ a hereditary torsion theory on the category σ[M] we use the concept of prime and semiprime module defined by Raggi et al. to introduce the concept of τ-pure prime radical Nτ(M)=Nτ as the intersection of all τ-pure prime submodules of M. We give necessary and sufficient conditions for the τ-nilpotence of Nτ(M). We prove that if M is a finitely generated R-module, progenerator in σ[M] and χ≠τ is FIS-invariant torsion theory such that M has τ-Krull dimension, then Nτ is τ-nilpotent.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66418891","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
On the structure of the algebra of derivations of cyclic Leibniz algebras 关于循环莱布尼兹代数的导数代数的结构
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1898
L. A. Kurdachenko, M. Semko, V. Yashchuk
{"title":"On the structure of the algebra of derivations of cyclic Leibniz algebras","authors":"L. A. Kurdachenko, M. Semko, V. Yashchuk","doi":"10.12958/adm1898","DOIUrl":"https://doi.org/10.12958/adm1898","url":null,"abstract":"We describe the algebra of derivation of finite-dimensional cyclic Leibniz algebra.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420121","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: 3
S-second submodules of a module 模块的s秒子模块
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1437
Faranak Farshadifar
{"title":"S-second submodules of a module","authors":"Faranak Farshadifar","doi":"10.12958/adm1437","DOIUrl":"https://doi.org/10.12958/adm1437","url":null,"abstract":"Let R be a commutative ring with identity and let M be an R-module. The main purpose of this paper is to introduce and study the notion of S-second submodules of an R-module M as a~generalization of second submodules of M.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66418003","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: 3
Diagonal torsion matrices associated with modular data 与模数据相关的对角扭转矩阵
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1368
G. Singh
{"title":"Diagonal torsion matrices associated with modular data","authors":"G. Singh","doi":"10.12958/adm1368","DOIUrl":"https://doi.org/10.12958/adm1368","url":null,"abstract":"Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group SL2(Z). Cuntz (2007) defined isomorphic integral modular data. Here we discuss isomorphic integral and non-integral modular data as well as non-isomorphic but closely related modular data. In this paper, we give some insights into diagonal torsion matrices associated to modular data.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417504","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 classifying the non-Tits P-critical posets 关于非tits p临界序集的分类
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1912
V. M. Bondarenko, M. Styopochkina
{"title":"On classifying the non-Tits P-critical posets","authors":"V. M. Bondarenko, M. Styopochkina","doi":"10.12958/adm1912","DOIUrl":"https://doi.org/10.12958/adm1912","url":null,"abstract":"In 2005, the authors described all introduced by them P-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by using computer algebra tools. In doing this, they defined and described the Tits P-critical posets as a special case of the P-critical posets. In this paper we classify all the non-Tits P-critical posets without complex calculations and without using the list of all P-critical ones.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420178","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: 2
Homotopy equivalence of normalized and unnormalized complexes, revisited 正则化与非正则化配合物的同伦等价
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1879
V. Lyubashenko, A. Matsui
{"title":"Homotopy equivalence of normalized and unnormalized complexes, revisited","authors":"V. Lyubashenko, A. Matsui","doi":"10.12958/adm1879","DOIUrl":"https://doi.org/10.12958/adm1879","url":null,"abstract":"We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the Dold-Kan correspondence for an idempotent complete additive category (kernels and cokernels are not required). The normalized complex is defined as the image of certain idempotent in the unnormalized complex. We prove that this idempotent is homotopic to identity via homotopy which is expressed via faces and degeneracies. Hence, the normalized and unnormalized complex are homotopy isomorphic to each other. We provide explicit formulae for the homotopy.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66420480","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
The structure of g-digroup actions and representation theory g群作用的结构与表征理论
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1741
J. G. Rodríguez-Nieto, O. Salazar-Díaz, R. Velásquez
{"title":"The structure of g-digroup actions and representation theory","authors":"J. G. Rodríguez-Nieto, O. Salazar-Díaz, R. Velásquez","doi":"10.12958/adm1741","DOIUrl":"https://doi.org/10.12958/adm1741","url":null,"abstract":"The aim of this paper is to propose two possible ways of defining a g-digroup action and a first approximation to representation theory of g-digroups.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419200","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
Cancellation ideals of a ring extension 环扩展的消去理想
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1424
S. Tchamna
{"title":"Cancellation ideals of a ring extension","authors":"S. Tchamna","doi":"10.12958/adm1424","DOIUrl":"https://doi.org/10.12958/adm1424","url":null,"abstract":"We study properties of cancellation ideals of ring extensions. Let R⊆S be a ring extension. A nonzero S-regular ideal I of R is called a (quasi)-cancellation ideal of the ring extension R⊆S if whenever IB=IC for two S-regular (finitely generated) R-submodules B and C of S, then B=C. We show that a finitely generated ideal I is a cancellation ideal of the ring extension R⊆S if and only if I is S-invertible.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417120","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
Common neighborhood spectrum of commuting graphs of finite groups 有限群交换图的共邻域谱
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1332
W. N. Fasfous, R. Sharafdini, R. K. Nath
{"title":"Common neighborhood spectrum of commuting graphs of finite groups","authors":"W. N. Fasfous, R. Sharafdini, R. K. Nath","doi":"10.12958/adm1332","DOIUrl":"https://doi.org/10.12958/adm1332","url":null,"abstract":"The commuting graph of a finite non-abelian group G with center Z(G), denoted by Γc(G), is a simple undirected graph whose vertex set is G∖Z(G), and two distinct vertices x and y are adjacent if and only if xy=yx. In this paper, we compute the common neighborhood spectrum of commuting graphs of several classes of finite non-abelian groups and conclude that these graphs are CN-integral.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417312","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: 4
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