Extensions of Z−ideals in MV−algebras

Document Type : Research Paper

Authors

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

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

3 Dept. of Math Shahid Bahonar University of Kerman

Abstract

In this paper, we introduce a special types of Z−ideals in MV −algebras and delve into their
properties. These particular ideals are thoroughly examined within the context of MV −chains,
semi-simple MV −algebras and Hyperarchimedean structures. Furthermore, we provide characterizations for these ideals, offering equivalent definitions that enhance our understanding of their nature. Our investigation also encompasses the relationships between these special Z−ideals and other types of ideals, such as the minimal prime ideals and the maximal ideals. Overall, this paper aims to provide a comprehensive analysis of special Z−ideals in MV −algebras.

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Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 4
July and August 2024
Pages 23-34

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