Z∘-ideals and Z-ideals in $MV$-algebras

The set of zero divisors of an $MV$-algebra is investigated. It is proved that the set of all zero divisors of an $MV$-algebra A is the union of all prime ideals of A. Next, Z∘-ideals and Z-ideals are introduced and their properties are studied. We examine the relationship between them and their relationship with the minimal prime ideals. We study their behavior under homomorphism of $ MV$-algebras. Also, we investigate in what conditions the annihilator of an ideal is a Z∘-ideal and Z-ideal.