Conjugate (nil) clean rings and Köthe’s problem

DOI10.1142/S0219498817500736zbMath1382.16036arXiv1605.09534OpenAlexW2963893021MaRDI QIDQ2988767

Jerzy Matczuk

Publication date: 19 May 2017

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09534

zbMATH Keywords

Köthe's problemnil clean ringsconjugate clean rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Conditions on elements (16U99)

Related Items (12)

Generalizations of UU-rings, UJ-rings and UNJ-rings ⋮ Nil 𝒢-cleanness and strongly nil 𝒢-cleanness of rings ⋮ A multiplicative dual of nil-clean rings ⋮ Unnamed Item ⋮ OnUJ-rings ⋮ On graded nil clean rings ⋮ On nil clean group rings ⋮ 𝑛-torsion clean rings ⋮ Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical ⋮ On rings with xn − x nilpotent ⋮ Group rings satisfying nil clean property ⋮ Nil-clean group rings

Cites Work

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• Nil-clean matrix rings
• Idempotents in ring extensions.
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• When is every matrix over a division ring a sum of an idempotent and a nilpotent?
• EXTENSIONS OF CLEAN RINGS
• On Uniquely Clean Rings
• On two open problems about strongly clean rings
• Lifting Idempotents and Exchange Rings
• RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT
• Logical connections between some open problems concerning nil rings

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