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Generalized Cline's Formula and Jacobson's Lemma in a Ring: 《Algebra Colloquium》2024年第3期407-416,共10页Huanyin Chen Marjan Sheibani; supported by the Natural Science Foundation of Zhejiang Province,China(No.LY21A010018).; We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson's lemma ...; 关键词：Cline's formula Jacobson's lemma generalized Drazin inverse Drazin inverse RING

(g,e)-Symmetric Rings: 《Algebra Colloquium》2024年第2期263-270,共8页Fanyun Meng Junchao Wei Nanqing Ding; supported by the Foundation of Natural Science of China(12301029,11171291);Natural Science Fund for Colleges and Universities in Jiangsu Province(11KJB110019 and 15KJB110023).; Let R be a ring and e,g in E(R),the set of idempotents of R.Then R is called(g,e)-symmetric if abc=0 implies gacbe=0 for any a,b,c∈R.Clearly,R is an e-symmetric ring if and only if R is a(1,e)-symmetric ring;in parti...; 关键词：IDEMPOTENT (g e)-symmetric ring Abel ring left semicentral

Gray Images of Constacyclic Codes over a Non-chain Extension of Z_(4): 《Algebra Colloquium》2024年第1期11-24,共14页Cruz Mohan Karthick Gowdhaman Durairajan Chinnapillai Jian Gao; Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/for a unit Λ=1+2u+2v in R.We define several Gray maps and ...; 关键词：non-chain ring linear code Ot-cyclic code Gray map (θ_(t) Λ)-cyclic code

Strongly Clean Matrix Rings over a Skew Monoid Ring: 《Algebra Colloquium》2023年第3期361-370,共10页Arezou Karimimansoub Mohammad-Reza(Rafsanjani)Sadeghi; Let R be a ring with an endomorphismσ,F∪{0}the free monoid generated by U={u1,…,ut}with 0 added,and M a factor of F obtained by setting certain monomials in F to 0 such that M^(n)=0 for some n.Then we can form the ...; 关键词：skew monoid rings strongly clean rings matrix rings

On the Grothendieck Ring of the Sequence of Walled Brauer Algebras: 《Algebra Colloquium》2023年第3期395-410,共16页Pei Wang Yanbo Li; In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a sequence of walled Brauer algebras. This approach also allows us to calculate the structure constants of multiplicat...; 关键词：walled Brauer algebra cellular algebra cell module Grothendieck ring

Duo Property Applied to Powers and Regular Elements: 《Algebra Colloquium》2023年第1期15-30,共16页TaiKeun Kwak Yang Lee Zhelin Piao Yeonsook Seo; The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called ri...; 关键词：right(exp-)DR ring regular element (weakly)right duo ring right quotient ring group ring

The Classification of Torsion-free TI-Groups: 《Algebra Colloquium》2022年第4期595-606,共12页Ryszard R.Andruszkiewicz Mateusz Woronowiczt; An abelian group A is called a TI-group if every associative ring with the additive group A is filial.The filiality of a ring R means that the ring R is associative and all ideals of any ideal of R are ideals in R.In ...; 关键词：torsion-free abelian group filial ring associative ring commutative ring additivegroupsof rings

Characterizations for the Core Invertibility and EP-ness Involving Projections: 《Algebra Colloquium》2022年第3期385-404,共20页Honglin Zou Dragana Cvetković-Ilić Jianlong Chen Kezheng Zuo; supported by the National Natural Science Foundation of China(No.11771076,11961076);the Ministry of Science,Technology and Development,Republic of Serbia(No.174007);the China Postdoctoral Science Foundation(No.2020M671281);the Research Project of Hubei Provincial Departmentof Education(No.B2019128).; In this paper we obtain some equivalent conditions for the core invertibility and EP-ness of 1−pq,1−pqp,p−pq and p−q,where p,q are projections in different settings,such as∗-rings,∗-reducing rings and C∗-algebras.More...; 关键词：core inverse PROJECTION EP element RING

Duo Property on the Monoid of Regular Elements: 《Algebra Colloquium》2022年第2期203-216,共14页Chan Yong Hong Hong Kee Kim Nam Kyun Kim Tai Keun Kwak Yang Lee; We study the right duo property on regular elements,and we say that rings with this property are right DR.It is first shown that the right duo property is preserved by right quotient rings when the given rings are rig...; 关键词：right DR ring right duo ring quotient ring (skew)polynomial ring group ring

On Annihilating Graphs Associated with Modules over Commutative Rings: 《Algebra Colloquium》2022年第2期281-296,共16页Rameez Raja Shariefuddin Pirzada; Let R be a commutative ring with unity,M be a unitary R-module and F be a simple connected graph.We examine different equivalence relations on subsets A_(f)(M)\{0},A_(s)(M)\{0}and A_(t)(M)/{0}of M,where A_(f)(M)is the...; 关键词：MODULE RING tensor product ANNIHILATOR GRAPH

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