Z◦−ideals in MV−algebras of continuous functions

Abstract

In this paper, we study MV?algebra of continuous functions C(X) and maximal ideals of C(X). Furthermore, Z?ideal and Z??ideal of C(X) are introduced and proved that every Z??ideal in C(X) is a Z?ideal but the converse is not true and every finitely generated Z?ideal is a basic Z??ideal. Also, we investigate meet and join of two Z?ideals (Z??ideal) of C(X). Complemented elements of C(X) are examined and their properties have been studied. In particular, the relationship between generated ideal by them and Z?ideals (Z??ideals) is proved. Finally, we investigate some property of Z??ideals in basically disconnected space and extremally disconnected space.