RESEARCH ARTICLE
A study on dual square free modules
M. Medina-Bárcenasa,
D. Keskin Tütüncüb,
Y. Kuratomic a Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudioy 18 Sur, Col.San Manuel, Ciudad Universitaria, 72570, Puebla, México
b Department of Mathematics, Hacettepe University, 06800, Beytepe, Ankara, Turkey
c Department of Mathematics, Faculty of Science, Yamaguchi University, Yamaguchi, Japan
Аннотация:
Let
$M$ be an
$H$-supplemented coatomic module with FIEP. Then we prove that
$M$ is dual square free if and only if every maximal submodule of
$M$ is fully invariant. Let
$M=\bigoplus_{i\in I} M_i$ be a direct sum, such that
$M$ is coatomic. Then we prove that
$M$ is dual square free if and only if each
$M_i$ is dual square free for all
$i\in I$ and,
$M_i$ and
$\bigoplus_{j\neq i}M_j$ are dual orthogonal. Finally we study the endomorphism rings of dual square free modules. Let
$M$ be a quasi-projective module. If
$\operatorname{End}_R(M)$ is right dual square free, then
$M$ is dual square free. In addition, if
$M$ is finitely generated, then
$\operatorname{End}_R(M)$ is right dual square free whenever
$M$ is dual square free. We give several examples illustrating our hypotheses.
Ключевые слова:
dual square free module, endoregular module, (finite) internal exchange property.
MSC: 16D40,
16D70 Поступила в редакцию: 11.12.2019
Исправленный вариант: 04.02.2021
Язык публикации: английский
DOI:
10.12958/adm1512