Modules and abelian groups with minimal (pure-) projectivity domains
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Date
2017
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Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Open Access Color
Green Open Access
Yes
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Abstract
In this paper we give a complete description of the projectively poor abelian groups and prove that there exists a pure projectively poor abelian group. We show that over a commutative Artinian ring every module having a projectively poor factor module by a pure submodule is itself projectively poor. We also give some other properties of pure projectively poor modules.
Description
ORCID
Keywords
Projectively poor module (abelian group), generic ring, pure p-generic (i-generic) module, pure-projectively poor module (abelian group), INJECTIVITY, RINGS, POOR, Pure p -Generic (i -Generic) Module, Projectively Poor Module (Abelian Group), Pure P-Generic (i-Generic) Module, Pure-Projectively Poor Module (Abelian Group), Generic Ring, pure \(p\)-generic (\(i\)-generic) module, General structure theorems for groups, generic ring, Homological and categorical methods for abelian groups, Module categories in associative algebras, projectively poor module (abelian group), Commutative Artinian rings and modules, finite-dimensional algebras, Projective and free modules and ideals in commutative rings, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), pure-projectively poor module (abelian group)
Fields of Science
0101 mathematics, 01 natural sciences
Citation
WoS Q
Scopus Q
OpenCitations Citation Count
5
Source
Journal of Algebra and Its Applications
Volume
16
Issue
11
Start Page
1750203
End Page
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CrossRef : 5
Scopus : 8
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