Results 31 to 40 of about 276,111 (308)

The relationships between clean rings, r-clean rings, and f-clean rings [PDF]

AIP Conference Proceedings, 2018
Suppose R is a ring with identity. R called a regular ring if each element is a regular element. A ring R is called an r-clean ring if every element in R can be expressed as the sum of a regular element and an idempotent element. An element in the ring R is called clean if it can be expressed as the sum of a unit element and an idempotent element, so ...
openaire   +1 more source

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   +1 more source

Nil-clean group rings

Journal of Algebra and Its Applications, 2016
An element [Formula: see text] of a ring [Formula: see text] is nil-clean, if [Formula: see text], where [Formula: see text] and [Formula: see text] is a nilpotent element, and the ring [Formula: see text] is called nil-clean if each of its elements is nil-clean. In [W. Wm. McGovern, S. Raja and A. Sharp, Commutative nil clean group rings, J.
Sahinkaya, Serap, Tang, Gaohua, Zhou, Yiqiang   +2 more
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On quotient clean hyperring [PDF]

Journal of Hyperstructures, 2015
In this paper, we introduce the notion of quotient Krasner hyperrings and prove that if I is a normal ideal of Krasner hyperring (R, +, ·), then quotient clean Krasner hyperring considered in [1] by Talebi et. al are just clean rings.
S. Ostadhadi-Dehkord
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

Mod-two cohomology of symmetric groups as a Hopf ring

, 2011
We compute the mod-2 cohomology of the collection of all symmetric groups as a Hopf ring, where the second product is the transfer product of Strickland and Turner.
Giusti, Chad, Salvatore, Paolo, Sinha, Dev   +2 more
core   +2 more sources

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

A biorenewable cyclobutane-containing building block synthesized from sorbic acid using photoenergy

iScience, 2022
Summary: A novel cyclobutane-containing diacid building block, CBDA-3, was synthesized from sorbic acid using clean, efficient [2 + 2] photocycloaddition.
Micah Mabin, Quintin Elliott, Zhihan Wang, Angel Ugrinov, Qianli R. Chu   +4 more
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

Factorizations of Matrices Over Projective-free Rings [PDF]

, 2014
An element of a ring $R$ is called strongly $J^{\#}$-clean provided that it can be written as the sum of an idempotent and an element in $J^{\#}(R)$ that commute.
Chen, H., Kose, H., Kurtulmaz, Y.
core