ON DUAL BAER MODULES

DOI10.1017/S0017089509990334zbMath1215.16007MaRDI QIDQ3564611

Rachid Tribak, Derya Keskin Tütüncü

Publication date: 26 May 2010

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

direct sumsDedekind domainsinjective moduleslifting modulesnon-cosingular modulesdual Baer moduleshereditary right Harada rings

Mathematics Subject Classification ID

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) Other classes of modules and ideals in associative algebras (16D80) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (36)

Purely Rickart and dual purely Rickart objects in Grothendieck categories ⋮ Strongly CS-Rickart and dual strongly CS-Rickart objects in abelian categories ⋮ Rickart and dual Rickart objects in abelian categories ⋮ Dual Rickart Modules ⋮ Supplement Submodules of Injective Modules ⋮ Some Generalizations of Quasi-Projective Modules ⋮ Split objects with respect to a fully invariant short exact sequence in abelian categories ⋮ Rickart and dual Rickart objects in abelian categories: transfer via functors ⋮ A note on noncosingular lifting modules. ⋮ On \(\mathcal T\)-\(\delta\)-noncosingular modules ⋮ Weak Rickart and dual weak Rickart objects in abelian categories ⋮ The Schröder–Bernstein problem for dual F-Baer modules ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Transfer of CS-Rickart and dual CS-Rickart properties via functors between Abelian categories ⋮ CS-Rickart and dual CS-Rickart objects in abelian categories ⋮ CS-Baer and dual CS-Baer objects in abelian categories ⋮ Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories ⋮ Direct sums of Rickart modules. ⋮ Strongly Rickart objects in abelian categories ⋮ Strongly Rickart objects in abelian categories: Applications to strongly regular and strongly Baer objects ⋮ On a class of dual Rickart modules ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ \(I_0^*\)-modules ⋮ CS-Rickart modules. ⋮ Unnamed Item ⋮ t-dual Baer modules and t-lifting modules. ⋮ When a (dual-)Baer module is a direct sum of (co-)prime modules ⋮ Quasi-dual Baer modules ⋮ Generating dual Baer modules via fully invariant submodules ⋮ On L-O-supplemented modules ⋮ On Weak Dual Rickart Modules and Dual Baer Modules ⋮ Modules Whose Endomorphism Rings are Von Neumann Regular ⋮ F-Baer objects with respect to a fully invariant short exact sequence in abelian categories

Cites Work

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• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Properties of direct summands of modules
• Baer and Quasi-Baer Modules
• MODULES FOR WHICH EVERY SUBMODULE HAS A UNIQUE COCLOSURE
• On 𝒦-Nonsingular Modules and Applications
• Modules Over Dedekind Rings and Valuation Rings
• On semilocal rings

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