\(n\)-almost prime submodules (Q395113)

The authors generalize and study the notion of \(n\)-almost prime ideals to the case of modules. Let \(R\) be a commutative ring. A proper submodule \(N\) of an \(R\)-module \(M\) is called an \(n\)-almost prime (submodule), if for \(r\in R\) and \(a\in N\) with \(ra\in N\backslash (N:M)^{n-1}N\), either \(a\in N\) or \(r\in (N:M)\), where \(n\) is a positive integer, and \((N:M)=\{r\in R|rM\subseteq N\}\).