Quelques remarques sur la notion de socle

DOI10.1080/00927878208822763zbMath0495.16030OpenAlexW2011442119MaRDI QIDQ3958622

Michel Hacque

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1080/00927878208822763

zbMATH Keywords

weak topologycontinuous endomorphismsfaithful modulehomogeneous componentstrictly continuous endomorphisms of finite rankidempotent homogeneous right soclenon-nilpotent minimal right idealprimitive rings with nonzero socletopological vector spaces over division rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Topological and ordered rings and modules (16W80) Artinian rings and modules (associative rings and algebras) (16P20) Representation theory of associative rings and algebras (16Gxx) Division rings and semisimple Artin rings (16Kxx)

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Une cohomologie galoisienne et non abélienne pour les corps gauches ⋮ Sous-anneaux a degres ⋮ Cohomologies des anneaux-groupes ⋮ Produits croisés mixtes: extensions de groupes et extensions d'anneaux ⋮ Structure globale des extensions regulieres galoisiennes ⋮ Théorie de Galois des anneaux presque-simples. (Galois theory of almost simple rings) ⋮ Prolongement d'isomorphismes et théorie de Galois. (Extension of isomorphisms and Galois theory) ⋮ Hacque-Amitsur rings ⋮ Armatures des extensions galoisiennes ⋮ Structure et synthese des extensions regulieres galoisiennes. I ⋮ Structure et synthese des extensions regulieres galoisiennes. II ⋮ Prolongement de derivations et theorie de galois ⋮ Endomorphism rings of modules and lattices of submodules ⋮ Isomorphismes et automorphismes des anneaux presque-simples ⋮ Completions intrinseques et co-intrinseques ⋮ Factorisations des extensions galoisiennes ⋮ Extensions des anneaux presque-simples ⋮ Anneaux fidelement representes sur leur socle droit

Cites Work

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• Rings faithfully represented on their left socle
• Rings in which minimal left ideals are projective
• On the theory of primitive rings
• On & - semisimple rings. A study of the socle of a ring
• On rings with essential socle
• Algèbre