Localization of modules and the central closure of rings

DOI10.1080/00927878108822655zbMath0461.16020OpenAlexW2051056448MaRDI QIDQ3910653

Robert Wisbauer

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1080/00927878108822655

zbMATH Keywords

Grothendieck categoryGoldie torsion theoryextended centroidlocalization theorycentral closure

Mathematics Subject Classification ID

Torsion theories, radicals (18E40) Prime and semiprime associative rings (16N60) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Localization and associative Noetherian rings (16P50) Localization of categories, calculus of fractions (18E35) Division rings and semisimple Artin rings (16Kxx)

Related Items (29)

On strongly prime rings and ideals ⋮ The rational Loewy series and nilpotent ideals of endomorphism rings ⋮ On SC-modules ⋮ Representation of rings with faithful polyform modules ⋮ A structure theorem for SI-Modules ⋮ \(\Sigma\)-extending modules ⋮ On weakly SI-modules ⋮ Injectivity and cogenerator properties of a ring as bimodule ⋮ Module categories with linearly ordered closed subcategories ⋮ A description of closed subcategories of σ[M] ⋮ Properly semiprime self-pp-modules ⋮ Direct sums of m-injective modules and module classes ⋮ Closed submodules of free modules over the endomorphism ring of a quasi-injective module ⋮ Endomorphism rings and dual modules ⋮ Modules arising from some relative injectives ⋮ On modules of finite length ⋮ Local-global results for modules over algebras and Azumaya rings ⋮ Endomorphism rings of modules and lattices of submodules ⋮ On semi-artinian \(V\)-modules ⋮ On endomorphism rings of quasiprojective modules ⋮ A central closure construction for certain algebra extensions. Applications to Hopf actions. ⋮ Kasch Modules and pV-Rings ⋮ Self-injective and PF endomorphism rings ⋮ Weakly semisimple modulesand density theory ⋮ Endomorphism rings and category equivalences ⋮ NATURAL CLASSES AND TORSION THEORIES ⋮ A Characterization of π-Complemented Algebras ⋮ On prime modules and rings ⋮ On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras

Cites Work

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• Jordan homomorphisms of semiprime rings
• Localization at epimorphisms and quasi-injectives
• Central embeddings in semi-simple rings
• Prime nonassociative algebras
• Nonassociative left regular and biregular rings
• Nonassociative rings satisfying normal polynomial identities
• Generalized centralizers of modules
• Prime rings satisfying a generalized polynomial identity
• Prime alternative rings. I, II
• Semiprime modules with maximum conditions
• Central closure of semiprime non-associative rings
• Erbliche moduln und nichtassoziative ringe
• An extension of the Jacobson density theorem
• Co-semisimple modules and nonassociative v-rings
• Localization and the gabriel-popescu embedding
• Relative localization; bimodules and semiprime P.I. rings
• Some Aspects of Ring Theory
• Endomorphism rings of torsionless modules
• Rings and modules of quotients

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