Weakly clean rings.

DOI10.1016/j.jalgebra.2013.10.034zbMath1314.16026OpenAlexW1981766751MaRDI QIDQ397968

Janez Šter

Publication date: 12 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2013.10.034

zbMATH Keywords

idempotentsmatrix ringsexchange rings\(\pi\)-regular ringssums of units\(\pi\)-regular elements\(C^*\)-algebras of real rank zerocorner ringsnon-unital ringssemiregular ringsweakly clean rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) General theory of (C^*)-algebras (46L05) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items

A generalization of -regular rings, Unnamed Item, Generalizing unit-regular rings and special clean elements

Cites Work

• Continuous modules are clean.
• On rings whose projective modules have the exchange property
• On pi-regular rings whose primitive factor rings are Artinian
• \(C^*\)-algebras of real rank zero
• Algebras over zero-dimensional rings
• Separative cancellation for projective modules over exchange rings
• Extensions of exchange rings
• On generalized regular rings
• Clean general rings.
• A CHARACTERIZATION OF UNIT REGULAR RINGS
• Corner Rings of a Clean Ring Need Not be Clean
• Lifting Idempotents and Exchange Rings
• Strongly clean rings and fitting's lemma
• Exchange rings, units and idempotents
• On Embedding Rings in Clean Rings
• Generalized regular rings