Relating properties of a ring with properties of matrix rings coming from Ornstein dual pairs

DOI10.1016/S0021-8693(03)00133-9zbMath1026.16014OpenAlexW1990158078MaRDI QIDQ1398149

Claudi Busqué, Juan Jacobo Simón

Publication date: 29 July 2003

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

Full work available at URL: https://doi.org/10.1016/s0021-8693(03)00133-9

zbMATH Keywords

idempotentsJacobson radicalvon Neumann regular ringssemisimple Artinian ringslattices of finitely generated left idealsOrnstein dual pairssemiregular matrix subrings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Ideals in associative algebras (16D25) Jacobson radical, quasimultiplication (16N20) Artinian rings and modules (associative rings and algebras) (16P20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dual vector spaces
• Categories of algebraic systems. Vector and projective spaces, semigroups, rings and lattices
• Finitely generated projective modules over row and column finite matrix rings
• Remarks on type I Baer and Baer\(^*\)-rings
• Semi-orthogonality in Rickart rings
• Modules with decompositions that complement direct summands
• Some Properties of Rings Reflected in Endomorphism Rings of Free Modules
• The Radical of the Row-Finite Matrices Over an Arbitrary Ring
• The Jacobson Radical of the Endomorphism Ring of a Projective Module
• Composition of binary quadratic forms
• Regular Endomorphism Rings of Free Modules
• An Ideal-Theoretic Characterization of the Ring of All Linear Transformations
• Intermediate rings between matrix rings and Ornstein dual pairs
• Relating properties of a ring and its ring of row and column finite matrices