Rings of idempotent stable range one.

DOI10.1007/s10468-011-9276-4zbMath1255.16013OpenAlexW2101225029MaRDI QIDQ434271

Zhou Wang, Dinesh Khurana, Jian-Long Chen, Tsit-Yuen Lam

Publication date: 10 July 2012

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-011-9276-4

zbMATH Keywords

regular elementsclean ringssemilocal ringsidempotent stable range oneunit regular rings

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) 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) Stable range conditions (19B10)

Related Items (13)

On idempotent stable range 1 matrices ⋮ Characterizations of special clean elements and applications ⋮ Perspective rings. ⋮ Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings ⋮ Characterizations of the commutators involving idempotents in certain subrings of $M_{2}(\mathbb{Z})$ ⋮ Special clean elements in rings ⋮ Rings of square stable range one ⋮ Regularity and related rings ⋮ On internally cancellable rings ⋮ SUMS OF UNITS IN RINGS ⋮ Lifting properties of formal triangular matrix rings ⋮ Characterizations and Direct Sums of Unit-Endoregular Modules ⋮ ON LIFTING OF STABLE RANGE ONE ELEMENTS

Cites Work

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• Bass's first stable range condition
• Cancellation of modules and groups and stable range of endomorphism rings
• Rings with many idempotents
• Clean matrices and unit-regular matrices.
• Rings with internal cancellation.
• On a substitution property of modules
• A CHARACTERIZATION OF UNIT REGULAR RINGS
• Lifting Idempotents and Exchange Rings
• A CRASH COURSE ON STABLE RANGE, CANCELLATION, SUBSTITUTION AND EXCHANGE

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