Weakly prime ternary subsemimodules of ternary semimodules

In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if N is a weakly prime subtractive ternary subsemimodule of a ternary R-semimodule M, then either N is a prime ternary subsemimodule or (N : M)(N : M)N = ۰. If N is a Q-ternary subsemimodule of  a ternary R-semimodule M, then a relation between weakly prime ternary subsemimodules of M containing N and weakly prime ternary subsemimodules of the quotient ternary R-semimodule M/N_{(Q)} is obtained.

کلیدواژه ها:

Entire ternary semimodule ، subtractive ternary subsemimodule ، partitioning ternary subsemimodule ، subtractive ternary subsemimodules ، partitioning ternary subsemimodules ، weakly prime ternary subsemimodule ، weakly prime ternary subsemimodules ، quotient ternary semimodule