Harada modules

Jayaraman, M; Vanaja, N.

doi:10.1080/00927870008827051

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Cited by 6 publications

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“…Somewhat unexpectedly it turns out that a ring is a left H-ring if and only if it is a right co-H-ring (see Oshiro [273]). Jayaraman and Vanaja [182] defined and studied H-modules and co-H-modules.…”

Section: Commentsmentioning

confidence: 99%

Lifting Modules

2006

Frontiers in Mathematics

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Section: Commentsmentioning

confidence: 99%

Lifting Modules

2006

Frontiers in Mathematics

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“…Azumaya (1974) proved that a projective module M is semiperfect if and only if every proper submodule of M is contained in a maximal submodule and every simple homomorphic image of M has a projective cover. Semiperfect modules were originally defined for projective modules by Mares, but it has been extended to arbitrary modules in Kasch (1982).…”

Section: Introductionmentioning

confidence: 99%

Semiperfect Modules with Respect to a Preradical

Özcan

Alkan

2006

Communications in Algebra

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In this article, we consider the module theoretic version of I-semiperfect rings R for an ideal I which are defined by Yousif and Zhou (2002). Let M be a left module over a ring R, N ∈ M , and M a preradical on M . We call N M -semiperfect in M if for any submodule K of N , there exists a decomposition K = A ⊕ B such that A is a projective summand of N in M and B ≤ M N . We investigate conditions equivalent to being a M -semiperfect module, focusing on certain preradicals such as Z M Soc, and M . Results are applied to characterize Noetherian QF-modules (with Rad M ≤ Soc M ) and semisimple modules. Among others, we prove that if every R-module M is Soc-semiperfect, then R is a Harada and a co-Harada ring.

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The Torsion Theory Cogenerated byM-Small Modules

Talebi

Vanaja

2002

Communications in Algebra

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Harada modules

Cited by 6 publications

References 8 publications

Lifting Modules

Lifting Modules

Semiperfect Modules with Respect to a Preradical

The Torsion Theory Cogenerated byM-Small Modules

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