ID | 49099 |
フルテキストURL | |
著者 |
Keskin Tütüncü, Derya
Department of Mathematics, Hacettepe University
Kuratomi, Yosuke
Kitakyushu National College of Technology
|
抄録 | 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.
|
キーワード | (generalized) mono-injective module
(weakly) mono-ojective module
extending module
|
発行日 | 2013-01
|
出版物タイトル |
Mathematical Journal of Okayama University
|
巻 | 55巻
|
号 | 1号
|
出版者 | Department of Mathematics, Faculty of Science, Okayama University
|
開始ページ | 117
|
終了ページ | 129
|
ISSN | 0030-1566
|
NCID | AA00723502
|
資料タイプ |
学術雑誌論文
|
言語 |
英語
|
著作権者 | Copyright©2013 by the Editorial Board of Mathematical Journal of Okayama University
|
論文のバージョン | publisher
|
査読 |
有り
|
Submission Path | mjou/vol55/iss1/5
|
JaLCDOI |