Some homological properties of amalgamated modules along an ideal

@article{Shoar2023,
abstract = {Let $R$ and $S$ be commutative rings with identity, $J$ be an ideal of $S$, $f \colon R \rightarrow S$ be a ring homomorphism, $M$ be an $R$-module, $N$ be an $S$-module, and let $\varphi \colon M \rightarrow N$ 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 $JN$.},
author = {Shoar, Hanieh, Salimi, Maryam, Tehranian, Abolfazl, Rasouli, Hamid, Tavasoli, Elham},
journal = {Czechoslovak Mathematical Journal},
keywords = {amalgamation of ring; amalgamation of module; Cohen-Macaulay; injective module; projective(flat) module},
language = {eng},
number = {2},
pages = {475-486},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some homological properties of amalgamated modules along an ideal},
url = {http://eudml.org/doc/299547},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Shoar, Hanieh
AU - Salimi, Maryam
AU - Tehranian, Abolfazl
AU - Rasouli, Hamid
AU - Tavasoli, Elham
TI - Some homological properties of amalgamated modules along an ideal
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 2
SP - 475
EP - 486
AB - Let $R$ and $S$ be commutative rings with identity, $J$ be an ideal of $S$, $f \colon R \rightarrow S$ be a ring homomorphism, $M$ be an $R$-module, $N$ be an $S$-module, and let $\varphi \colon M \rightarrow N$ 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 $JN$.
LA - eng
KW - amalgamation of ring; amalgamation of module; Cohen-Macaulay; injective module; projective(flat) module
UR - http://eudml.org/doc/299547
ER -