Some classes of state ideals in state $MV$-algebras

In this paper, we introduce some types of state ideals in state $MV$-algebras such as: obstinate state ideals, primary state ideals and Boolean state ideals in state $MV$-algebras. We present some characterizations of them and investigate some relations between them. We consider the quotient algebras induced by these state ideals and prove some related theorems.