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ID 41400
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Author
Baba, Yoshitomo
Yamazaki, Takeshi
Abstract
The concept of almost N-projectivity is defined in [5] by M. Harada and A. Tozaki to translate the concept "lifting module" in terms of homomorphisms. In [6, Theorem 1] M. Harada defined a little weaker condition "almost N-simple-projecive" and gave the following relationship between them: For a semiperfect ring R and R-modules M and N of finite length, M is almost N-projective if and only if M is almost N-simple-projective. We remove the assumption "of finite length" and give the result in Theorem 5 as follows: For a semiperfect ring R, a finitely generated right R-module M and an indecomposable right R-module N of finite Loewy length, M is almost N-projective if and only if M is almost N-simple-projective. We also see that, for a semiperfect ring R, a finitely generated R-module M and an R-module N of finite Loewy length, M is N-simple-projective if and only if M is N-projective.
Keywords
ring
module
almot projective
almost simple-projective
Published Date
2011-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume53
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
101
End Page
109
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol53/iss1/6
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