Orders in rings without identity

DOI10.1080/00927879008824062zbMath0719.16022OpenAlexW1982447505MaRDI QIDQ5751028

J. B. Fountain, Victoria Gould

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1080/00927879008824062

zbMATH Keywords

regular ringsemigroupring of quotientsmultiplicative semigroupleft ordercompletely 0-simplesquare cancellable elementleft square cancellableright square cancellable

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Semigroup rings, multiplicative semigroups of rings (20M25) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Ore rings, multiplicative sets, Ore localization (16U20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (23)

Local orders in Jordan algebras ⋮ Left orders in strongly regular rings ⋮ Left orders in Abelian regular rings ⋮ Structure theorem for prime rings satisfying a generalized identity ⋮ MOORE–PENROSE LOCALIZATION ⋮ Towards a Goldie theory for Jordan pairs ⋮ Orders in semiprime rings with minimal condition for principal right ideals ⋮ Orders in primitive rings with non-zero socle and posner's theorem ⋮ A new approach to orders in simple rings with minimal one-sided ideals ⋮ Independence algebras, basis algebras and the distributivity condition ⋮ Left orders in regular \({\mathcal H}\)-semigroups. I ⋮ Algebras of quotients of path algebras. ⋮ ORDERS IN RINGS WITH INVOLUTION ⋮ A tribute to John B. Fountain ⋮ Orders in regular rings with minimal condition for principal right ideals ⋮ THE MAXIMAL LEFT QUOTIENT RINGS OF ALTERNATIVE RINGS ⋮ Faith-Utumi Theorem for Associative Pairs ⋮ Fountain-Gould left orders for associative pairs. ⋮ Unnamed Item ⋮ Goldie theorems for associative pairs ⋮ LEFT QUOTIENT RINGS OF ALTERNATIVE RINGS ⋮ Ordering Orders and Quotient Rings ⋮ Maximal orders in semigroups¹

Cites Work

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• A representation of a semigroup by a semigroup of matrices over a group with zero
• One-to-one partial right translations of a right cancellative semigroup
• Abundant Semigroups
• STRAIGHT LEFT ORDERS IN RINGS
• Orders in semiprime rings with minimal condition for principal right ideals
• On a new proof of Litoff's theorem

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