Theoretical study demonstrates algebraic properties of weak Z-ideals in MV-algebras, uncovering new classifications for prime and minimal prime ideals.
In this paper, the arranged element is introduced in MV -algebras, and its characteristics are studied. It is proved that an MV -algebra A is an MV -chain if and only if every nonzero element is an arranged element. In the continuation, weak Z∘ Z ∘ -ideals are defined and equivalent definitions of weak Z∘ Z ∘ -ideals are provided. Their relationships with existing notions such as Z∘ Z ∘ -ideals and Z∘J Z J ∘ -ideals are examined. This analysis makes it possible to establish new classifications of prime and minimal prime ideals. Additionally, properties of annihilators in MV -algebras are investigated.
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Forouzesh et al. (2026) studied this question.
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