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On the Generalized Strongly Nil-Clean Property of Matrix Rings
《Algebra Colloquium》2021年第4期625-634,共10页Aleksandra S.Kostic Zoran Z.Petrovic Zoran S.Pucanovic Maja Roslavcev 
supported by Ministry of Educations,Science and Technological Development of Republic of Serbia Project#174032.
Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n×n matrix A over R is expressible as a sum A=E1+…+Es+N of(commuting)idempotent matrices Ei and a nilpotent...
关键词：idempotent matrix nilpotent matrix nil-clean ring matrix ring 
Nil-Clean Rings with Involution被引量：2
《Algebra Colloquium》2021年第3期367-378,共12页Jian Cui Guoli Xia Yiqiang Zhou 
This research was supported by Anhui Provincial Natural Science Foundation(No.2008085MA06);the Key Project of Anhui Education Committee(No.gxyqZD2019009)(for Cui);a Discovery Grant from NSERC of Canada(for Xia and Zhou).
A*-ring R is called a nil *-clean ring if every element of R is a sum of a projection and a nilpotent.Nil*-clean rings are the version of nil-clean rings introduced by Diesl.This paper is about the nil*-clean property...
关键词：IDEMPOTENT NILPOTENT PROJECTION nil-clean ring *-ring nil*-clean ring matrix ring 
Schubert Class and Cyclotomic NilHecke Algebras
《Algebra Colloquium》2021年第3期379-398,共20页Kai Zhou Jun Hu 
The research was supported by the National Natural Science Foundation of China(No.11525102).
Let l and n be positive integers such that l≥n,and let Gn,l be the Grassmannian which consists of the set of n-dimensionsil subspaces of C^(l),There is a Z-graded algebra isomorphism between the cohomology H*(Gn,l,Z)...
关键词：cyclotomic nilHecke algebras GRASSMANNIANS Schur polynomials 
A Generalization of Strongly Nil Clean Rings被引量：4
《Algebra Colloquium》2018年第4期585-594,共10页Jian Cui Xiaobin Yin 
the National Natural Science Foundation of China (No.11401009);the Key Natural Science Foundation of Anhui Educational Committee (No.KJ2014A082);the Anhui Provincial Natural Science Foundation (No.1408085QA01).
Generalizing the notion of strongly nil clean rings,we introduce strongly quasinil clean rings.Some fundamental properties and equivalent characterizations of this class of rings are provided.By means of g-Drazin inve...
关键词：STRONGLY quasi-nil CLEAN RING STRONGLY NIL CLEAN RING STRONGLY CLEAN RING g-Drazin inverse 
Structure of Zhou Nil-clean Rings
《Algebra Colloquium》2018年第3期361-368,共8页Huanyin Chen Marian Sheibani 
The authors are grateful to the referee for his/her careful the paper, and for the invaluable comments which improve our presentation reading of author H.Y. Chen was supported by the Natural Science Foundation of Zhejiang （No. LY17A010018）, China. The first Province
A ring R is Zhou nil-clean if every element in R is the sum of two tripotents and a nilpotent that commute. Homomorphic images of Zhou nil-clean rings are explored. We prove that a ring R is Zhou nil-clean if and only...
关键词：tripotent NILPOTENT homomorphic images generalized matrix rings Zhou nil-clean rings 
Nil Clean Graphs of Rings被引量：1
《Algebra Colloquium》2017年第3期481-492,共12页Dhiren Kumar Basnet Jayanta Bhattacharyya 
In this article, we define the nil clean graph of a ring R. The vertex set is the ring R, and two ring elements a and b are adjacent if and only if a ＋ b is nil clean in R. Graph theoretic properties like the girth, ...
关键词：nil clean ring weak nil clean ring nil clean graph 
On Evolution Algebras
《Algebra Colloquium》2014年第2期331-342,共12页J.M. Casas M. Ladra B.A. Omirov U.A. Rozikov 
The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triang...
关键词：evolution algebra nil algebra right nilpotent algebra group of endomor-phisms classification 
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