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Abstract
<p>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|M<sub>1</sub> and f ◦ h2 = g|N<sub>2</sub> . 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.</p>
Journal
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- Mathematical Journal of Okayama University
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Mathematical Journal of Okayama University 52 (1), 111-122, 2010-01
Department of Mathematics, Faculty of Science, Okayama University
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Details 詳細情報について
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- CRID
- 1390853649555103488
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- NII Article ID
- 120002309701
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- NII Book ID
- AA00723502
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- ISSN
- 00301566
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- CiNii Articles