On & - semisimple rings. A study of the socle of a ring

DOI10.1080/00927878008822497zbMath0434.16020OpenAlexW2079078557MaRDI QIDQ3872608

Giuseppe Baccella

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1080/00927878008822497

zbMATH Keywords

semisimple modulessimple modulesidempotent idealshereditary torsion theoryright Gabriel topologyright soclesemisimple two-sided idealsTTF-class

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Conditions on elements (16U99) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items

\(\aleph\)-QF 3 rings with zero singular ideal, Socle chains of Abelian regular semiartinian rings., On socle chains of semiartinian rings with primitive factors Artinian, Rings with flat left socle^∗, The structure of qf-3 rings with zero singular ideal^(∗), Semiartinian rings whose loewy factors are nonsingular, Relative injectivity and chain conditions, Projective dimension of singular modules over nonsingular rings with essential socle, NOTES ON COTORSION MODULES, On Lifting Projective Modules Modulo an Essential Socle, Rings Related to Mininjective and Min-Flat Modules, Rings with Projective Socle, Rings with the Kazimirsky condition and rings with projective socle, Cotorsion modules and relative pure-injectivity, Exchange property and the natural preorder between simple modules over semi-Artinian rings, Min-Flat Modules and Min-Coherent Rings, Generalized V-rings and von Neumann regular rings, Quelques remarques sur la notion de socle

Cites Work

• Unnamed Item
• A Wedderburn-Artin-Jacobson structure theorem
• Rings in which minimal left ideals are projective
• Semi-Simplicity Relative to Kernel Functors
• Divisible and Codivisible Modules.
• On rings with essential socle