Rings with internal cancellation.

DOI10.1016/j.jalgebra.2004.07.032zbMath1076.16004OpenAlexW2045244266MaRDI QIDQ1764840

Dinesh Khurana, Tsit-Yuen Lam

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.07.032

zbMATH Keywords

regular elementsfinitely generated projective modulesexchange ringscomplex group algebrasunit-regular elementsstable range conditionslifting idempotentspseudo-similaritiesidempotent generated right idealsinternal direct sum cancellationregular stable range 1unique generator property

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Ideals in associative algebras (16D25) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Stable range conditions (19B10)

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Cites Work

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• Projective modules over group rings and maximal orders
• Pseudosimilarity and cancellation of modules
• A note on the group structure of unit regular ring elements
• Euler characteristics and characters of discrete groups
• Separative cancellation for projective modules over exchange rings
• Stable range one for exchange rings
• Hilbert modules and modules over finite von Neumann algebras and applications to \(L^ 2\)-invariants
• Exercises in classical ring theory.
• Wavelet filter functions, the matrix completion problem, and projective modules over \(C(\mathbb{T}^n)\).
• Quaternionic bundles on algebraic spheres
• Completion of diagrams by automorphisms and Bass' first stable range condition
• Projective modules over Witt rings
• Lifting idempotents in associative pairs
• Cancellation of Azumaya algebras
• Exchange rings and decompositions of modules
• \(K\)-theory and stable algebra
• Pseudo-similarity and partial unit regularity
• Strongly 𝜋-regular rings have stable range one
• Vector Bundles and Projective Modules
• Units and One-Sided Units in Regular Rings
• Lifting Idempotents and Exchange Rings
• Pseudo-Similarity for Matrices Over a Field
• Dedekind Finite Rings and a Theorem of Kaplansky
• On Related Power Comparability of Modules
• On stable range conditions
• A CRASH COURSE ON STABLE RANGE, CANCELLATION, SUBSTITUTION AND EXCHANGE
• On ExchangeQB-Rings
• Stable Range One for Rings with many Idempotents
• On the decomposition of modules
• Composition of binary quadratic forms
• Elementary Divisors and Modules
• Exchange rings having stable range one

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