(n − 1, n)-weakly prime submodules in direct product of modules

Let n≥2 be a positive integer, R be a commutative ring with identity and M be a unitary R-module . In this paper we study the ( n − 1 , n )-weakly prime submodules of direct product of modules. Also, we show that for some special cases, every proper submodule is ( n − 1 , n ) -weakly prime.