• PRIME TERNARY SUBSEMIMODULES IN TERNARY SEMIMODULES

Abstract

Let be a ternary semimodule over a ternary semiring . We introduce the notion of prime ternary subsemimodule of which is a generalization of a prime subsemimodule introduced by Atani [1] and hence we extend the results of semimodules, ternary semirings and partial semimodules to ternary semimodules over ternary semirings. Prime ternary subsemimodules of a multiplication ternary semimodule over ternary semiring are characterized. Also we prove prime avoidance theorem for ternary semimodules over ternary semirings.