A Special Type of Ideals in MV-algebras of Continuous Functions

In this paper, Z-ideals and Z°-ideals in MV-algebras of continuous functions C(X) are investigated. We introduce a special type of Z-ideals and Z°-ideals in MV-algebras of continuous functions C(X), and call them ZJ-ideals and Z°J-ideals. In particular, equivalent definitions have been provided for them and the relationship between them has been examined; their relationship with the minimal prime ideal has been investigated, too. The meet and the join of two ZJ-ideals and Z°J-ideals are studied and we prove that the join of twoZJ-ideals is a ZJ-ideal whenever the continuous functions are defined on the real numbers R or the functions are defined on a compact metric space X. We also study when the annihilator of a subset of an MV-algebras of continuous functions is a ZJ-ideal or a Z°J-ideal.. © 2023, College Publications. All rights reserved.