A study of antiprincipal ideals in  <i>MV</i> -algebras

Abstract This paper introduces antiprincipal ideals as a new concept in infinite MV -algebras. We prove that these ideals constitute a particular subclass of weak Z °-ideals and investigate their relationships with other classes of ideals, such as prime and minimal prime ideals. In addition, we characterize the elements belonging to these antiprincipal ideals. Several examples from different MV -algebras are presented to illustrate their structural properties and to provide a better understanding of ideals that are not principal in MV -algebras.