State extended ideals in state MV-algebras
In this paper, we introduce the notion of state extended ideal associated to a subset of state MV-algebras and investigate the related properties. A characterization of this state extended ideal in a state MV-algebras is given. In addition, we study the relation between state extended ideals and state prime ideals, state maximal ideal in a state MV-algebra. We show that if f:A→B is state homomorphism MV-algebra such that f(A^' )=B', then we have (1) If I is a state stable relative to B'⊆B, then f^(-1) (I) is a state stable relative to A'⊆A. (2) If f is an onto and I is a state stable relative to A'⊆A, Ker(f)⊆I, then f(I) is a state stable relative to B'⊆B. In finally, we define state stable ideals and we show that the class S(B) of all state stable ideals relative to B⊆A is also a complete Heyting algebra, for a state MV-algebra (A,σ).
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