Cancellation of projective modules over regular rings with comparability

DOI10.1016/0022-4049(95)00034-8zbMath0851.16008OpenAlexW2060660845WikidataQ126437424 ScholiaQ126437424MaRDI QIDQ1916144

Pere Ara, K. C. O'Meara, D. V. Tyukavkin

Publication date: 24 November 1996

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

Full work available at URL: https://doi.org/10.1016/0022-4049(95)00034-8

zbMATH Keywords

stable range\(s\)-comparabilityunit-regular ringsfinitely generated projective right modulesdirectly finite regular rings\((s:t)\)-comparability

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Grothendieck groups, (K)-theory, etc. (16E20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (24)

On regular rings with s-comparability ⋮ Comparability, Stability, and Completions of Ideals ⋮ Unnamed Item ⋮ A CLOSURE OPERATION IN RINGS ⋮ Von Neumann regular rings satisfying weak comparability. ⋮ On products of three triangular matrices over associative rings ⋮ The structure of countably generated projective modules over regular rings ⋮ Unnamed Item ⋮ On Von Neumann Regular Rings With Weak Comparability II ⋮ EXCHANGE RINGS WITH GENERAL ALEPH-NOUGHT-COMPARABILITY ⋮ UNIT-REGULAR RINGS SATISFYING WEAK COMPARABILITY ⋮ Comparability and \(s\)-comparability of modules over exchange rings ⋮ On Regular Rings Satisfying Almost Comparability ⋮ Ideal-comparability over regular rings. ⋮ Generalized Stable Regular Rings ⋮ On generalized stable rings ⋮ Strong separativity over exchange rings ⋮ Separative cancellation for projective modules over exchange rings ⋮ Regular Rings Satisfying Generalized Almost Comparability ⋮ The State Space ofK₀of Exchange Rings ⋮ Separative Cancellation over Regular Rings ⋮ An infinite analogue of rings with stable rank one ⋮ Separativity of modules with finite exchange property ⋮ REGULAR RINGS WITH COMPARABILITY AND SOME RELATED PROPERTIES

Cites Work

• Unnamed Item
• On regular subdirect products of simple Artinian rings
• Products of idempotents in regular rings. II
• On regular rings with stable range 2
• Cancellation of modules and groups and stable range of endomorphism rings
• Simple regular rings satisfying weak comparability
• Injective positively ordered monoids. I
• Rank functions and \(K_0\) of regular rings
• Simple regular rings with a unique rank function
• The almost isomorphism relation for simple regular rings
• Semiartinian \(V\)-rings and semiartinian von Neumann regular rings
• \(K\)-theoretically simple von Neumann regular rings
• Free and residually artinian regular rings
• Stable rank of rings and dimensionality of topological spaces
• Depth of Idempotent-Generated Subsemigroups of a Regular Ring
• Torsion in K₀ of unit-regular rings
• Elementary Divisors and Modules

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