Rings in which elements are uniquely the sum of an idempotent and a unit that commute.

DOI10.1016/j.jpaa.2008.06.004zbMath1162.16019OpenAlexW2162969293WikidataQ112881990 ScholiaQ112881990MaRDI QIDQ958120

Zhou Wang, Jian-Long Chen, Yiqiang Zhou

Publication date: 2 December 2008

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2008.06.004

zbMATH Keywords

unitsidempotentstriangular matrix ringsstrongly clean ringsuniquely clean rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Units, groups of units (associative rings and algebras) (16U60)

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Cites Work

• Unnamed Item
• Group rings in which every element is uniquely the sum of a unit and an idempotent.
• Clean general rings.
• COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT
• On Strongly Clean Matrix and Triangular Matrix Rings
• STRONGLY CLEAN POWER SERIES RINGS
• On strongly πregular rings and homomorphisms into them
• Strongly clean rings and fitting's lemma
• On abelian π-regular rings
• RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT
• On the Structure of Algebraic Algebras and Related Rings