Strongly prime submodules and pseudo-valuation modules (Q2920214)

Let \(R\) be an integral domain. If \(R\)-module \(N\) is a proper submodule of \(M\), \((N:M)=P\) and \(r\in R\), \(m\in M\) and \(rm\in N\) imply that either \(m\in N\) or \(r\in P\), then \(P\) turns out to be a prime ideal of \(R\), and \(N\) is called a \(P\)-prime submodule of \(M\). Thus prime submodules are a generalization of prime ideals.NEWLINENEWLINEIn the paper under review, the authors generalize the notion of strongly prime ideal to a prime submodule of a torsion free \(R\)-module and give some characterizations of them.