Document Type : Original Article
Department of Mathematics, Farhangian University, Tehran, Iran
In , by using an MV-semiring and an MV-algebra, we introduced the new definition of MV-semimodule and studied some of their basic properties. In this paper, we study and present definitions of primary ideals of MV-semirings, decomposition of ideals in MV-semirings, primary A-ideals of MV -semimodules, and decomposition of A-ideals in MV-semimodules. Then we present some conditions that an A-ideal can have a reduced primary decomposition.