ID | 49099 |
FullText URL | |
Author |
Keskin Tütüncü, Derya
Kuratomi, Yosuke
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Abstract | In [5] and [6], we have introduced a couple of relative generalized
epi-projectivities and given several properties of these projectivities.
In this paper, we consider relative generalized injectivities that are
dual to these relative projectivities and apply them to the study of direct
sums of extending modules. Firstly we prove that for an extending
module N, a module M is N-injective if and only if M is mono-Ninjective
and essentially N-injective. Then we define a mono-ojectivity
that plays an important role in the study of direct sums of extending
modules. The structure of (mono-)ojectivity is complicated and hence it
is difficult to determine whether these injectivities are inherited by finite
direct sums and direct summands even in the case where each module
is quasi-continuous. Finally we give several characterizations of these
injectivities and find necessary and sufficient conditions for the direct
sums of extending modules to be extending.
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Keywords | (generalized) mono-injective module
(weakly) mono-ojective module
extending module
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Published Date | 2013-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume55
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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 | 117
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End Page | 129
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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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Copyright Holders | Copyright©2013 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol55/iss1/5
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JaLCDOI |