State radical ideals in state MV-algebras

In this paper, the notions of prime state ideals and state semi-maximal ideals of state MV -algebras are introduced. We  prove prime state ideal theorem and we show that a state MV -algebra A is semi-simple if and only if A has no state  infinitesimals. We introduce the concept of state radical of state ideals in a state MV -algebra, we present a characterization  of a state radical ideal. We show that the set of state radicals of state ideals in (A, σ) is a Heyting algebra.