On properties of closed sets in the Zariski topology of MV -algebras
نویسندگان
1 Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132. 84084 Fisciano, SA, Italy.
2 Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye.
3 Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
4 Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132. 84084 Fisciano, SA, Italy
doi
10.22111/ijfs.2026.9911چکیده
This paper presents a localized approach to the Zariski topology by restricting the spectral space to specific subsetsof prime ideals within an MV -algebra. We investigate a particular class of Zariski-closed sets and demonstrate thatthey form a lattice under set inclusion. A distinguished filter within this lattice is then examined, and its algebraicproperties are analyzed in detail. Building on this framework, we introduce the concept of vX-ideals, a new type of idealdefined in terms of these closed sets. We explore their algebraic behavior, including interactions with minimal primeideals and their stability under homomorphisms. The study reveals new structural insights into Zariski-closed sets andtheir connections to broader ideal-theoretic constructs. The final diagram synthesizes these findings, offering a unifiedperspective and laying the foundation for further exploration of topological and algebraic properties in MV -algebras.
