Rings with finite essential socle

DOI10.1090/S0002-9939-97-03747-7zbMath0871.16012OpenAlexW1564101281MaRDI QIDQ3127278

Pedro A. Guil Asensio, José L. Gómez Pardo

Publication date: 8 April 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03747-7

zbMATH Keywords

direct summandssimple right modulesinjective envelopesfinitely generated right modulesQF-ringscyclic right modulesessential right socleright injective cogenerator ringsright \(CS\)-ringsessential finitely generated projective submodulesright \(FGF\)-ringsright \(PF\)-ringsright self-injectivity

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Quasi-Frobenius rings (16L60) Noncommutative local and semilocal rings, perfect rings (16L30)

Related Items

Some results on the quotient of co-m modules, On modules and rings in which complements are isomorphic to direct summands, New characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture, On continuous rings, Embeddings in free modules and Artinian rings, WEAKLY CONTINUOUS AND C2-RINGS, Annihilators and the CS-condition, WHEN IS A SEMIPERFECT RING RIGHT PF?, Soc-Injective Rings and Modules*

Cites Work

• Commutative rings for which every continuous module is quasi-injective
• Serial rings and finitely presented modules
• A generalization of quasi-Frobenius rings
• RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
• On Semiregular Rings whose Finitely Generated Modules Embed in Free Modules
• Essential embedding of cyclic modules in projectives
• Radical properties of perfect modules.
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