On δ-semiperfect modules

A submodule N of a module M is δ-small in M if N+X≠M for any proper submodule X of M with M∕X singular. A projective δ-cover of a module M is a projective module P with an epimorphism to M whose kernel is δ-small in P. A module M is called δ-semiperfect if every factor module of M has a projective δ...

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Bibliographic Details
Published inCommunications in algebra Vol. 46; no. 11; pp. 4965 - 4977
Main Authors Nguyen, Hau Xuan, Koşan, M. Tamer, Zhou, Yiqiang
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.11.2018
Subjects
Primary: 16D99
projective δ-cover
semiperfect module
δ-Lifting module
δ-semiperfect module
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Summary:A submodule N of a module M is δ-small in M if N+X≠M for any proper submodule X of M with M∕X singular. A projective δ-cover of a module M is a projective module P with an epimorphism to M whose kernel is δ-small in P. A module M is called δ-semiperfect if every factor module of M has a projective δ-cover. In this paper, we prove various properties, including a structure theorem and several characterizations, for δ-semiperfect modules. Our proofs can be adapted to generalize several results of Mares [ 8 ] and Nicholson [ 11 ] from projective semiperfect modules to arbitrary semiperfect modules.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1459650