Extensions of Z−ideals in MV−algebras
نویسندگان
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
doi
10.22111/ijfs.2024.48312.8498چکیده
In this paper, we introduce a special types of Z−ideals in MV −algebras and delve into theirproperties. 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.
