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Strongly 2T - Clean Rings [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
An element a in a ring R is referred to be strongly 2T-clean (2 – STC element for short), a = Ω-Λ+u, where Ω,Λ are idempotent elements and u is a unit elements of order three.
Zeina Hamady, Nazar Shuker
doaj   +3 more sources

Strongly Invo. T- Clean Rings [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
In this paper, we present the idea of a strongly invo. T-clean rings, which we define as rings with every a in R having the formula a = t + v, where t is a tripotent and v is an order two unit that commute.
Rand Alneamy, Nazar Shuker
doaj   +3 more sources

Super strongly clean group rings

Discussiones Mathematicae - General Algebra and Applications, 2023
Amit B. Singh, Susheel Kumar
doaj   +3 more sources

Strongly nil *-clean rings [PDF]

Journal of Algebra Combinatorics Discrete Structures and Applications, 2017
A $*$-ring $R$ is called {\em strongly nil $*$-clean} if every element of $R$ is the sum of a projection and a nilpotent element that commute with each other.
Chen, Huanyin, Harmancı, Abdullah, Özcan, A. Çiğdem   +2 more
core   +6 more sources

STRONGLY RIGHT SINGULAR CLEAN RINGS [PDF]

International Journal of Apllied Mathematics, 2021
: Let R be an associative ring with identity. Then R is said to be strongly right singular clean, if every element of R can be expressed as a sum of a right singular element and an idempotent that commute.
F. Rashedi
semanticscholar   +2 more sources

The Strongly Nil-Clean Rings Of Order Two Units [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
If every element of a ring R is the sum of idempotent and nilpotent that commute, then the ring is said to be a strongly nil-clean. Further features of a strongly nil-clean ring are given in this paper.
Samira Toma, Nazar Shuker
doaj   +2 more sources

On strongly $$\sum $$ ∑ -m-clean rings

Indian Journal of Pure and Applied Mathematics, 2022
Let \(R\) be a commutative ring with identity, \(U(R)\) the set of all units of \(R\) and \(J(R)\) the Jacobson radical of \(R\). In this paper, the author defined the notions of strongly \(\sum\)-\(m\)-clean ring and \(m\)-semiboolean ring as natural generalizations of the concept of strongly \(m\)-clean and semiboolean rings respectively. Let \(m\geq
M. A. S. Moutui
semanticscholar   +2 more sources

A class of uniquely (strongly) clean rings

TURKISH JOURNAL OF MATHEMATICS, 2014
In this paper we call a ring R dr-clean if every element is the sum of an idempotent and an element in d(RR) where d(RR) is the intersection of all essential maximal right ideals of R. If this representation is unique (and the elements commute) for every element we call the ring uniquely (strongly) dr-clean.
Orhan Gürgün, A. Ç. Özcan
semanticscholar   +4 more sources

Some families of strongly clean rings

Linear Algebra and its Applications, 2007
A ring R with identity is called strongly clean if every element of R is the sum of an idempotent and a unit that commute with each other. For a commutative local ring R and for an arbitrary integer n ⩾ 2 , the paper deals with the question whether the ...
Xiande Yang, Yiqiang Zhou
semanticscholar   +2 more sources

Abel Rings and Super-Strongly Clean Rings

Annals of the Alexandru Ioan Cuza University - Mathematics, 2015
In this note, we first show that a ring R is Abel if and only if the 2 × 2 upper triangular matrix ring ( R R 0 R ) over R is quasi-normal. Next, we give the notion of super-strongly clean ring (that is, an Abel clean ring), which is inbetween uniquely ...
Y. Qu, Junchao Wei
semanticscholar   +2 more sources