On Uniquely Clean Rings

DOI10.1080/00927870903451959zbMath1251.16027arXiv1406.7472OpenAlexW2104944565MaRDI QIDQ3081520

Huanyin Chen

Publication date: 8 March 2011

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

Full work available at URL: https://arxiv.org/abs/1406.7472

zbMATH Keywords

nilpotent elementsBoolean ringscentral idempotentsexchange ringsAbelian ringsuniquely clean ringsuniquely nil clean rings

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (12)

Rings in which the power of every element is the sum of an idempotent and a unit ⋮ Characterizations of special clean elements and applications ⋮ Unnamed Item ⋮ Conjugate (nil) clean rings and Köthe’s problem ⋮ WHEN IS AN ABELIAN WEAKLY CLEAN RING CLEAN? ⋮ USING IDEALS TO PROVIDE A UNIFIED APPROACH TO UNIQUELY CLEAN RINGS ⋮ Commutative weakly nil clean unital rings. ⋮ Commutative rings whose proper homomorphic images are nil clean ⋮ 𝑛-torsion clean rings ⋮ Unnamed Item ⋮ Weak clean index of a ring ⋮ On weakly clean and weakly exchange rings having the strong property

Cites Work

• Unnamed Item
• Group rings in which every element is uniquely the sum of a unit and an idempotent.
• On weak \(\pi\)-regularity of rings whose prime ideals are maximal
• Weakly clean rings and almost clean rings
• On the structure of exchange rings
• COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT
• Clean Elements in Commutative Reduced Rings
• A CLASS OF EXCHANGE RINGS
• On abelian π-regular rings
• RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT
• ON THE MAXIMALITY OE PRIME IDEALS IN EXCHANGE RINGS

This page was built for publication: On Uniquely Clean Rings