ID | 33498 |
FullText URL | |
Author |
Tütüncü, Derya Keskin
Kuratomi, Yosuke
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Abstract | A module M is said to be generalized N-projective (or N-dual ojective) if, for any epimorphism g : N → X and any homomorphism f : M → X, there exist decompositions M = M1 ⊕ M2, N = N1 ⊕ N2, a homomorphism h1 : M1 → N1 and an epimorphism h2 : N2 → M2 such that g ◦ h1 = f|M1 and f ◦ h2 = g|N2 . This relative projectivity is very useful for the study on direct sums of lifting modules (cf. [5], [7]). In the definition, it should be noted that we may often consider the case when f to be an epimorphism. By this reason, in this paper we define relative (strongly) generalized epi-projective modules and show several results on this generalized epi-projectivity. We apply our results to the known problem when finite direct sums M1⊕· · ·⊕Mn of lifting modules Mi (i = 1, · · · , n) is lifting. |
Keywords | (strongly) generalized epi-projective module
lifting module
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Published Date | 2010-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume52
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 111
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End Page | 122
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol52/iss1/9
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JaLCDOI |