ID | 41400 |
FullText URL | |
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 |
English
|
Copyright Holders | Editorial Board of Mathematical Journal of Okayama University
|
File Version | publisher
|
Refereed |
True
|
Submission Path | mjou/vol53/iss1/6
|
JaLCDOI |