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Some homological properties of amalgamated modules along an ideal

Hanieh Shoar; Maryam Salimi; Abolfazl Tehranian; Hamid Rasouli; Elham Tavasoli — 2023

Czechoslovak Mathematical Journal

Let $R$ and $S$ be commutative rings with identity, $J$ be an ideal of $S$ , $f : R \to S$ be a ring homomorphism, $M$ be an $R$ -module, $N$ be an $S$ -module, and let $ϕ : M \to N$ be an $R$ -homomorphism. The amalgamation of $R$ with $S$ along $J$ with respect to $f$ denoted by $R ⋈^{f} J$ was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of $(R ⋈^{f} J)$ -module called the amalgamation of $M$ and $N$ along $J$ with respect to $ϕ$ , and denoted by $M ⋈^{ϕ} J N$ . We study some homological properties of the $(R ⋈^{f} J)$ -module $M ⋈^{ϕ} J N$ . Among other results,...

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