S-spectral topology in MV -algebras

In this paper, we introduce new classes of ideals, called S-prime ideals and S-maximal ideals,based on a ∧-closed system S. The connection between these ideals and classical prime idealsis examined, and it is shown that every S-prime ideal constitutes a specific type of prime ideal.Moreover, it is proven that any proper ideal disjoint from S is contained in an S-prime ideal.The behavior of S-prime ideals is further analyzed in the setting of quotient MV -algebras, andtheir properties under isomorphisms are investigated. In the final part of the study, the complete∧-closed system S is introduced, and a new topology, called the S-spectral topology, is defined usingS and the family of S-ideals. Several topological properties of this space, including the Hausdorff,T۰, and T۱ separation axioms, are discussed.

کلیدواژه ها:

MV -algebra ، ∧-closed system ، S-prime ideal ، S-spectral topology