Results 241 to 250 of about 182,974 (268)

A note on strongly regular near-rings

Publicationes Mathematicae Debrecen, 2022
In this interesting short note, the authors prove that if N is a strongly regular near-ring, then the maximum condition on ideals implies the minimum condition on ideals. In ring theory, it is well known that if every nilpotent element is in the center then every idempotent is central. Hence a regular ring without nilpotent element is strongly regular.
Reddy, Y. V., Murty, C. V. L. N.
openaire   +1 more source

On strongly \(\pi\)-regular rings and periodic rings

Mathematical Journal of Okayama University, 1985
A ring R is called normal if every idempotent is central. Let \(P=\{x\in R:\) \(xe=x\) for some idempotent e and \(xy=0\) iff \(ey=0\) for \(y\in R\}\). An element \(x\in R\) is called strongly regular if for some y in R \(x=x^ 2y=yx^ 2\). It is called regular if \(xyx=x\) for some y. It is called \(\pi\)-regular (resp. strongly \(\pi\)-regular) if \(x^
openaire   +3 more sources

On some extensions of strongly unit nil-clean rings

Journal of Algebra and its Applications
An element $x \in R$ is considered (strongly) nil-clean if it can be expressed as the sum of an idempotent $e \in R$ and a nilpotent $b \in R$ (where $eb = be$).
Ruhollah Barati
semanticscholar   +1 more source

On Strongly -Regular Rings and Strongly Commuting -Regular Rings

Journal of Garmian University, 2017
Abdullah Abdul-Jabbar, Lavan Mustafa
openaire   +1 more source

On stable range one property and strongly $$\pi $$ π -regular rings

Afrika Matematika, 2020
Rachida El Khalfaoui, N. Mahdou
semanticscholar   +1 more source

Locally distributive spectral categories and strongly regular rings. : 1967 Reports of the Midwest Category Seminar

, 1967
J. Roos
semanticscholar   +1 more source

A symmetric generalization of π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}-regular rings

Ricerche di Matematica, 2021
P. Danchev
semanticscholar   +1 more source

Some Two-Weight Codes Over Chain Rings and their Strongly Regular Graphs

Graphs and Combinatorics
Minjia Shi, Ruowen Liu, Patrick Solé
semanticscholar   +1 more source

Strongly Additively Regular Rings and Graphs

2019
A commutative ring R is said to be additively regular if for each pair of elements \(f,g\in R\) with f regular, there is an element \(t\in R\) such that \(g+ft\) is regular. For any commutative ring R, the polynomial ring \(R[{\scriptstyle \mathrm {X}}]\) is additively regular, moreover if \(deg(g)
openaire   +1 more source

A symmetric generalization of $$\pi $$-regular rings

Ricerche Di Matematica, 2021
Peter V Danchev
exaly