| Title:
|
Some homological properties of amalgamated modules along an ideal (English) |
| Author:
|
Shoar, Hanieh |
| Author:
|
Salimi, Maryam |
| Author:
|
Tehranian, Abolfazl |
| Author:
|
Rasouli, Hamid |
| Author:
|
Tavasoli, Elham |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
73 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
475-486 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ and $S$ be commutative rings with identity, $J$ be an ideal of $S$, $f \colon R \to S$ be a ring homomorphism, $M$ be an $R$-module, $N$ be an $S$-module, and let $\varphi \colon M \to N$ be an $R$-homomorphism. The amalgamation of $R$ with $S$ along $J$ with respect to $f$ denoted by $R \bowtie ^{f} J$ was introduced by M. D'Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of $(R \bowtie ^{f} J)$-module called the amalgamation of $M$ and $N$ along $J$ with respect to $\varphi $, and denoted by $M \bowtie ^{\varphi } JN$. We study some homological properties of the $(R \bowtie ^{f} J)$-module $M \bowtie ^{\varphi } JN$. Among other results, we investigate projectivity, flatness, injectivity, Cohen-Macaulayness, and prime property of the $(R \bowtie ^{f} J)$-module $M \bowtie ^{\varphi } JN$ in connection to their corresponding properties of the $R$-modules $M$ and $JN$. (English) |
| Keyword:
|
amalgamation of ring |
| Keyword:
|
amalgamation of module |
| Keyword:
|
Cohen-Macaulay |
| Keyword:
|
injective module |
| Keyword:
|
projective(flat) module |
| MSC:
|
13A15 |
| MSC:
|
13C10 |
| MSC:
|
13C11 |
| MSC:
|
13C14 |
| MSC:
|
13C15 |
| idZBL:
|
Zbl 07729518 |
| idMR:
|
MR4586905 |
| DOI:
|
10.21136/CMJ.2023.0411-21 |
| . |
| Date available:
|
2023-05-04T17:46:09Z |
| Last updated:
|
2025-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151668 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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