Some remarks on \(S\)-strongly prime submodules (Q6566493)

In the paper under review, the authors introduced and studied the notion of \(S\)-strongly prime submodule. Let \(R\) be a commutative ring \(S\subseteq R\) be a multiplicatively closed subset of \(R\) and \(M\) be an \(R\)-module. A submodule \(N\) of \(M\) with \((N:_RM)\cap S=\emptyset\) is said to be \emph{\(S\)-strongly prime}, if there exists an \(s\in S\) such that whenever \(((N+Rx):_RM)y\subseteq N\), then \(sx\in N\) or \(sy\in N\) for all \(x,y\in M\). The author investigated the notion of \(S\)-strongly prime submodule in module homomorphism, localization, quotient modules, Cartesian product and amalgamated modules along an ideal.