Results 31 to 40 of about 60,182 (167)

COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS

Ural Mathematical Journal, 2019
A ring \(R\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \(R\) and each abelian group \(G\), we find only in terms of \(R\), \(G\) and their sections a ...
Peter V. Danchev
doaj   +1 more source

Nil clean rings

Journal of Algebra, 2013
Given a ring \(R\), one says that an element \(r\in R\) is \textit{clean} if \(r=e+u\) where \(e\in R\) is an idempotent and \(u\) is a unit of \(R\). Moreover, the element \(r\) is \textit{strongly clean} if the idempotent and unit can be chosen to commute.
openaire   +2 more sources

THE CLEANNESS OF THE SUBRINGS OF M_2 (Z_P)

Barekeng
Let  be a ring. Ring  is said to be a clean ring if every element of R can be expressed as the sum of a unit and an idempotent element. Furthermore, there are r-clean rings. An r-clean ring is a generalization of a clean ring.
Shinta Nur Alfiana, Nikken Prima Puspita, Widowati Widowati   +2 more
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On clean ideals

International Journal of Mathematics and Mathematical Sciences, 2003
We introduce the notion of clean ideal, which is a natural generalization of clean rings. It is shown that every matrix ideal over a clean ideal of a ring is clean. Also we prove that every ideal having stable range one of a regular ring is clean.
Huanyin Chen, Miaosen Chen
doaj   +1 more source

Strongly nil *-clean rings

Journal of Algebra Combinatorics Discrete Structures and Applications, 2017
A *-ring $R$ is called a strongly nil-*-clean ring if every element of $R$ is the sum of a projection and a nilpotent element that commute with each other. In this article, we show that $R$ is a strongly nil-*-clean ring if and only if every idempotent in $R$ is a projection, $R$ is periodic, and $R/J(R)$ is Boolean.
HARMANCİ, Abdullah, CHEN, Huanyin, OZCAN, A. Cigdem   +2 more
openaire   +4 more sources

On γ-Clean Rings

Science Journal of University of Zakho, 2017
In this paper we introduce the concept of -clean ring and we discuss some relations between - clean ring and other rings with explaining by some examples. Also, we give some basic properties of it.
Shaimaa S. Esa, Hewa S. Faris
doaj   +1 more source

A Note on Commutative Nil-Clean Corners in Unital Rings

Известия Иркутского государственного университета: Серия "Математика", 2019
We shall prove that if $R$ is a ring with a family of orthogonal idempotents $\{e_i\}_{i=1}^n$ having sum $1$ such that each corner subring $e_iRe_i$ is commutative nil-clean, then $R$ is too nil-clean, by showing that this assertion is actually ...
P.V. Danchev
doaj   +1 more source

Weakly clean rings

Journal of Algebra, 2014
Building on his ground-breaking work from ``Corner rings of a clean ring need not be clean'' [Commun. Algebra 40, No. 5, 1595-1604 (2012; Zbl 1247.16034)], the author continues his study of weakly clean rings and elements. Let \(R\) be a ring. The author calls \(a\in R\) \textit{weakly clean} exactly when the diagonal matrix \(\text{diag}(a,0)\) is ...
openaire   +2 more sources

ON YAQUB NIL-CLEAN RINGS

Mathematical Reports, 2022
"A ring R is Yaqub nil-clean if a+a3 or a−a3 is nilpotent for all a ∈ R. We prove that a ring R is a Yaqub nil-clean ring if and only if R ∼= R1,R2,R3,R1 ×R2 or R1×R3, where R1/J(R1) is Boolean, R2/J(R2) is a Yaqub ring, R3/J(R3) ∼= Z5 and each J(Ri) is nil, if and only if J(R) is nil and R/J(R) is isomorphic to a Boolean ring R1, a Yaqub ring R2, Z5 ...
Chen, Huanyin, Abdolyousefi, Marjan Sheibani   +1 more
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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
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