Strong cleanness of generalized matrix rings over a local ring.

DOI10.1016/J.LAA.2012.06.035zbMATH Open1258.16032OpenAlexW2037151546MaRDI QIDQ1758458

Gaohua Tang, Yiqiang Zhou

Publication date: 9 November 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.06.035

zbMATH Keywords

unitsidempotentsstrongly clean ringscommutative local ringsstrongly \(\pi\)-regular ringsgeneralized matrix rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Noncommutative local and semilocal rings, perfect rings (16L30) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Local rings and semilocal rings (13H99)

Cites Work

• Title not available (Why is that?)
• Modules over formal matrix rings.
• Strong cleanness of the \(2\times 2\) matrix ring over a general local ring.
• Diagonalizability of idempotent matrices over noncommutative rings
• Strongly clean matrix rings over local rings.
• Strongly clean triangular matrix rings over local rings.
• Strongly clean matrix rings over commutative local rings.
• When is the \(2\times 2\) matrix ring over a commutative local ring strongly clean?
• On two open problems about strongly clean rings
• On Strongly Clean Matrix and Triangular Matrix Rings
• Isomorphism of generalized matrix rings
• STRONGLY CLEAN POWER SERIES RINGS
• Strongly clean rings and fitting's lemma

Related Items (14)

Strongly clean matrix rings over local rings. ⋮ A class of formal matrix rings. ⋮ On UQ rings ⋮ Formal matrices and their determinants ⋮ STRONG P-CLEANNESS OF TRIVIAL MORITA CONTEXTS ⋮ The group \(K_0\) of a generalized matrix ring ⋮ On the binary system of factors of formal matrix rings ⋮ Calculation of the group \(K_1\) of a generalized matrix ring ⋮ Determinants of generalized matrices of order 2 ⋮ Formal matrices and rings close to regular ⋮ Certain strongly clean matrices over local rings ⋮ STRONGLY CLEAN MATRIX RINGS OVER NONCOMMUTATIVE LOCAL RINGS ⋮ Quasipolar Property of Generalized Matrix Rings ⋮ Formal matrix rings and their isomorphisms.

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