Relative splitting properties with applications to endomorphism rings

DOI10.1080/00927878808823691zbMath0652.16017OpenAlexW2142457354MaRDI QIDQ3797340

J. Asensio Mayor, José L. Gómez Pardo

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1080/00927878808823691

zbMATH Keywords

projective moduleinjectivequotient categorysingular submodulequotient ringendomorphism ringdirect summandtrace idealGabriel topology\({\mathcal F}\)-SI ringsrelative splitting propertysingular splitting property

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Free, projective, and flat modules and ideals in associative algebras (16D40) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90)

Cites Work

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• Semiperfect modules relative to a torsion theory
• The quotient category of a Morita context
• Some aspects of Goldie's torsion theory
• The singular submodule splits off
• On commutative rings over which the singular submodule is a direct summand for ervery module
• U-distinguished modules
• V-rings relative to gabriel topologies
• Spectral gabriel topologies and relative singular functors
• The splitting property for graded rings

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