|
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
Abstract:
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.
Keywords:
dual square free module, endoregular module, (finite) internal exchange property.
Received: 11.12.2019 Revised: 04.02.2021
Citation:
M. Medina-Bárcenas, D. Keskin Tütüncü, Y. Kuratomi, “A study on dual square free modules”, Algebra Discrete Math., 32:2 (2021), 267–279
Linking options:
https://www.mathnet.ru/eng/adm821 https://www.mathnet.ru/eng/adm/v32/i2/p267
|
Statistics & downloads: |
Abstract page: | 65 | Full-text PDF : | 28 | References: | 9 |
|