Fuzzy Semi-Maximal and Fuzzy Radical Ideals in MV-Algebras

Fereshteh Forouzesh ()
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Fereshteh Forouzesh: Faculty of Mathematics and Computing, Higher Education Complex of Bam, Bam Kerman, Iran

New Mathematics and Natural Computation (NMNC), 2018, vol. 14, issue 01, 73-89

Abstract: In this paper, we introduce the notions of fuzzy semi-maximal ideals and fuzzy primary ideals of an MV-algebra and investigate some of their properties. Also, several characterizations of these fuzzy ideals are given. In addition, we show that μ is a fuzzy semi-maximal ideal of A if and only if A∕μ is a semi-simple MV-algebra and μ is a fuzzy primary ideal of A if and only if A∕μ is local MV-algebra. By using the notions of the maximal and normal fuzzy semi-maximal ideals, we show that under certain conditions a fuzzy semi-maximal ideal is two-valued and takes the values 0 and 1. The radical of a fuzzy ideal is defined as against the (maximal) radical of a fuzzy ideal and some of their properties are proved.

Keywords: Fuzzy semi-maximal ideal; fuzzy primary ideal; fuzzy radical (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S1793005718500060

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