Z ◦−ideals in MV −algebra 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 investigated meet and join of two Z−ideal (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.