A new approach to orders in simple rings with minimal one-sided ideals

DOI10.1007/BF02573396zbMath0701.16021MaRDI QIDQ913921

Victoria Gould, Mario Petrich

Publication date: 1990

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

Full work available at URL: https://eudml.org/doc/135054

zbMATH Keywords

maximal conditionprime ringsannihilatorsGoldie dimensionmultiplicative semigroupFaith- Utumi theoremorders in ringsOrders in simple ringsRees-matrix ringsring of linear transformationssemigroup of quotients

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) General structure theory for semigroups (20M10) Prime and semiprime associative rings (16N60) Semigroup rings, multiplicative semigroups of rings (20M25) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Localization and associative Noetherian rings (16P50)

Related Items (4)

Structure theorem for prime rings satisfying a generalized identity ⋮ Orders in semiprime rings with minimal condition for principal right ideals ⋮ Left orders in regular \({\mathcal H}\)-semigroups. I ⋮ Left orders in regular rings with minimum condition for principal one-sided ideals

Cites Work

• Completely 0-simple semigroups of quotients
• The translational hull in semigroups and rings
• The Structure of Prime Rings Under Ascending Chain Conditions
• Orders in regular rings with minimal condition for principal right ideals
• STRAIGHT LEFT ORDERS IN RINGS
• Orders in semiprime rings with minimal condition for principal right ideals
• Orders in rings without identity
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