On some classes of expansions of ideals in MV -algebras

In this paper, we introduce the notions of expansion of ideals in MV-algebras, (τ,σ)−primary, (τ,σ)-obstinate and (τ,σ)-Boolean in MV−algebras. We investigate the relations of them. For example, we show that every (τ,σ)-obstinate ideal of an MV− algebra is (τ,σ)-primary and (τ,σ)-Boolean. In particular, we define an expansion σy of ideals in an MV−algebra. A characterization of expansion ideal with respect to σy is given. Finally, we show that the class C(σy) of all constant ideals relative to σy is a Heyting algebra.