Coretractable modules relative to a submodule
Let $R$ be a ring and $M$ a right $R$-module. Let $N$ be a proper submodule of $M$. We say that $M$ is $N$-coretractable (or $M$ is coretractable relative to $N$) provided that, for every proper submodule $K$ of $M$ containing $N$, there is a nonzero homomorphism $f:M/K\rightarrow M$. We present som...
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| Format: | Article |
| Language: | English |
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Yildiz Technical University
2019-05-01
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| Series: | Journal of Algebra Combinatorics Discrete Structures and Applications |
| Online Access: | http://jacodesmath.com/index.php/jacodesmath/article/view/241 |
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doaj-7a20824043514457a729b038263859d42020-11-24T21:32:49ZengYildiz Technical UniversityJournal of Algebra Combinatorics Discrete Structures and Applications2148-838X2019-05-0162120Coretractable modules relative to a submoduleAli Reza Moniri Hamzekolaee0Yahya Talebi1Assistant Professor of Algebra, Ring and Module Theory, Department of Math University of MazandaranAssociate Professor of Algebra, Ring and Module Theory, Department of Math University of MazandaranLet $R$ be a ring and $M$ a right $R$-module. Let $N$ be a proper submodule of $M$. We say that $M$ is $N$-coretractable (or $M$ is coretractable relative to $N$) provided that, for every proper submodule $K$ of $M$ containing $N$, there is a nonzero homomorphism $f:M/K\rightarrow M$. We present some conditions that a module $M$ is coretractable if and only if $M$ is coretractable relative to a submodule $N$. We also provide some examples to illustrate special cases.http://jacodesmath.com/index.php/jacodesmath/article/view/241 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ali Reza Moniri Hamzekolaee Yahya Talebi |
| spellingShingle |
Ali Reza Moniri Hamzekolaee Yahya Talebi Coretractable modules relative to a submodule Journal of Algebra Combinatorics Discrete Structures and Applications |
| author_facet |
Ali Reza Moniri Hamzekolaee Yahya Talebi |
| author_sort |
Ali Reza Moniri Hamzekolaee |
| title |
Coretractable modules relative to a submodule |
| title_short |
Coretractable modules relative to a submodule |
| title_full |
Coretractable modules relative to a submodule |
| title_fullStr |
Coretractable modules relative to a submodule |
| title_full_unstemmed |
Coretractable modules relative to a submodule |
| title_sort |
coretractable modules relative to a submodule |
| publisher |
Yildiz Technical University |
| series |
Journal of Algebra Combinatorics Discrete Structures and Applications |
| issn |
2148-838X |
| publishDate |
2019-05-01 |
| description |
Let $R$ be a ring and $M$ a right $R$-module. Let $N$ be a proper submodule of $M$. We say that $M$ is $N$-coretractable (or $M$ is coretractable relative to $N$) provided that, for every proper submodule $K$ of $M$ containing $N$, there is a nonzero homomorphism $f:M/K\rightarrow M$. We present some conditions that a module $M$ is coretractable if and only if $M$ is coretractable relative to a submodule $N$. We also provide some examples to illustrate special cases. |
| url |
http://jacodesmath.com/index.php/jacodesmath/article/view/241 |
| work_keys_str_mv |
AT alirezamonirihamzekolaee coretractablemodulesrelativetoasubmodule AT yahyatalebi coretractablemodulesrelativetoasubmodule |
| _version_ |
1725955716144955392 |