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Title: Rings and modules characterized by opposites of FP-injectivity
Authors: Büyükaşık, Engin
Kafkas Demirci, Gizem
Keywords: Injective modules
FP-injective modules
Subpurity domain
Flat modules
Publisher: Korean Mathematical Society
Abstract: Let R be a ring with unity. Given modules M-R and N-R, M-R is said to be absolutely N-R-pure if M circle times N -> L circle times N is a monomorphism for every extension L-R of M-R. For a module M-R, the subpurity domain of M-R is defined to be the collection of all modules N-R such that M-R is absolutely N-R-pure. Clearly M-R is absolutely F-R-pure for every flat module F-R, and that M-R is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, M-R is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. R-R is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is Priifer if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.
ISSN: 1015-8634
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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