A survey of strongly clean rings.
type: Item
instance of: scholarly article
title: A survey of strongly clean rings.
zbMATH Open document ID: 1202.16032
author: Xiande Yang
published in: Acta Applicandae Mathematicae
publication date: 2009-12-09T00:00:00Z
review text: The author gives an account of the results on strongly clean rings. The author introduces some main results and some interesting questions on the following subjects: (1) Strongly \(\pi\)-regular rings vs strongly clean rings; (2) Clean rings vs strongly clean rings; (3) Necessary conditions for a matrix ring to be strongly clean; (4) Strongly clean matrix rings over commutative rings; (5) Strongly clean matrix rings over local rings; (6) Strongly clean matrix rings over other strongly clean rings; (7) Strongly clean triangular matrix rings; (8) Incidence rings over strongly clean rings; (9) Strongly clean power series rings; (10) Uniquely clean rings and uniquely strongly clean rings; (11) Strongly clean general rings.
reviewed by: Tong Wenting
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16W60
zbMATH DE Number: 5644655
zbMATH Keywords: strongly clean rings
zbMATH Keywords: strongly clean general rings
zbMATH Keywords: power series rings
zbMATH Keywords: matrix rings
MaRDI profile type: Publication
full work available at URL: s10440-008-9364-6
OpenAlex ID: W2065330917
cites work: COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT
cites work: Q4023148
cites work: Strongly 𝜋-regular rings have stable range one
cites work: Topological Representation of Algebras
cites work: On injective and surjective endomorphisms of finitely generated modules
cites work: Non-commutative Henselian rings.
cites work: When is \(C(X)\) a clean ring?
cites work: On Maximally Central Algebras
cites work: Q5831378
cites work: Strongly clean triangular matrix rings over local rings.
cites work: Strongly clean matrix rings over commutative local rings.
cites work: On strongly πregular rings and homomorphisms into them
cites work: A CHARACTERIZATION OF UNIT REGULAR RINGS
cites work: Addendum to ``Examples of semiperfect rings''
cites work: STRONGLY CLEAN POWER SERIES RINGS
cites work: Group rings in which every element is uniquely the sum of a unit and an idempotent.
cites work: On Strongly Clean Matrix and Triangular Matrix Rings
cites work: When is the \(2\times 2\) matrix ring over a commutative local ring strongly clean?
cites work: Rings in which elements are uniquely the sum of an idempotent and a unit that commute.
cites work: A Question on Strongly Clean Rings
cites work: Q3808246
cites work: Strong Cleanness of Matrix Rings Over Commutative Rings
cites work: Q4106702
cites work: Q5598409
cites work: Q4317713
cites work: Q3994935
cites work: Q4107488
cites work: ON STRONGLY CLEAN MATRIX RINGS
cites work: EXTENSIONS OF CLEAN RINGS
cites work: Q3982326
cites work: Topological Representation of Algebras. II
cites work: Strongly clean matrix rings over local rings.
cites work: Generalized regular rings
cites work: Clean Semiprimef-Rings with Bounded Inversion
cites work: On the Theory of Henselian Rings
cites work: Lifting Idempotents and Exchange Rings
cites work: Strongly clean rings and fitting's lemma
cites work: Q5292125
cites work: On Regular Rings
cites work: On two open problems about strongly clean rings
cites work: Some families of strongly clean rings.
cites work: Strong cleanness of the \(2\times 2\) matrix ring over a general local ring.
DOI: 10.1007/S10440-008-9364-6
description: scientific article; zbMATH DE number 5644655