Decomposition of A-ideals in MV-modules

In this paper, by considering the notion of MV-modules, we present definition of radical of an ideal in MV-algebras by prime ideals that in last was defined by maximal ideals. Also, we define the notions of primary and P-primary A-ideals in MV-modules. Then we show that under conditions, if an A-ideal has a primary decomposition, then it has a reduced primary decomposition. Finally, we characterize proper A-ideals that have a reduced primary decomposition.