On some classes of expansions of ideals in MV-algebras

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

On some classes of expansions of ideals in MV-algebras Keywords:

Expansion of an ideal , sigma)-primary , sigma)-obstinate , (tau , sigma)-Boolean , Heyting algebra