Universal localizations embedded in power-series rings

DOI10.1515/FORUM.2007.015zbMath1136.16021OpenAlexW2090287985MaRDI QIDQ5435168

Pere Ara, Warren Dicks

Publication date: 14 January 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum.2007.015

zbMATH Keywords

invertible matricescompletionsinvertible elementsdivision ringsvon Neumann regular ringspower series ringsinverses of elementsuniversal localizationsfree ringsdivision closuresRF-ringsstably flat rings

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Free nonabelian groups (20E05) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (4)

Blanchfield and Seifert algebra in high-dimensional boundary link theory. I: Algebraic \(K\)-theory ⋮ Obtaining free group algebras in division rings generated by group graded rings ⋮ Free group algebras in division rings with valuation I ⋮ Module theory over Leavitt path algebras and \(K\)-theory.

Cites Work

• Ordering coproducts of groups and semigroups
• Free algebras over Bezout domains are Sylvester domains
• Sylvester domains
• Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring
• Noncommutative localisation in algebraic \(K\)-theory. I
• NON-COMMUTATIVE CHARACTERISTIC POLYNOMIALS AND COHN LOCALIZATION
• On a Theorem of Ian Hughes About Division Rings of Fractions
• A jacobian conjecture for free associative algebras
• The Cohn localization of the free group ring
• Fields of Fractions for Group Algebras of Free Groups
• The Residual Nilpotence of Wreath Products
• Division Rings of Fractions for Group Rings

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