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https://hdl.handle.net/11147/9086
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. | URI: | https://doi.org/10.4134/BKMS.b180325 https://hdl.handle.net/11147/9086 |
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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RINGS AND MODULES.pdf | 322.5 kB | Adobe PDF | View/Open |
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