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

Author

Listed:
  • Fereshteh Forouzesh

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

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.

Suggested Citation

  • Fereshteh Forouzesh, 2018. "Fuzzy Semi-Maximal and Fuzzy Radical Ideals in MV-Algebras," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 73-89, March.
    • Handle: RePEc:wsi:nmncxx:v:14:y:2018:i:01:n:s1793005718500060
    DOI: 10.1142/S1793005718500060
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