On properties of closed sets in the Zariski topology of MV -algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132. 84084 Fisciano, SA, Italy

2 Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

3 Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye.

4 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

5 Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences (SIMATS) Chennai India.

10.22111/ijfs.2026.9911

Abstract

This paper presents a localized approach to the Zariski topology by restricting the spectral space to specific subsets
of prime ideals within an MV -algebra. We investigate a particular class of Zariski-closed sets and demonstrate that
they form a lattice under set inclusion. A distinguished filter within this lattice is then examined, and its algebraic
properties are analyzed in detail. Building on this framework, we introduce the concept of vX-ideals, a new type of ideal
defined in terms of these closed sets. We explore their algebraic behavior, including interactions with minimal prime
ideals and their stability under homomorphisms. The study reveals new structural insights into Zariski-closed sets and
their connections to broader ideal-theoretic constructs. The final diagram synthesizes these findings, offering a unified
perspective and laying the foundation for further exploration of topological and algebraic properties in MV -algebras.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 3
May and June 2026
Pages 15-29

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