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On Engel Fuzzy Subpolygroups

Author

Listed:
  • R. A. Borzooei

    (Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran)

  • E. Mohammadzadeh

    (#x2020;Department of Mathematics, Faculty of Science, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran)

  • Violeta Fotea

    (#x2021;Faculty of Mathematics, Alexandru Ioan Cuza University, 700506 Iasi, Romania)

Abstract

In this paper, by considering the notions of polygroup and Engel group, we introduce the concept of Engel fuzzy subpolygroups. In this regard, by a normal Engel fuzzy subpolygroup μ of P and β*, the fundamental relation on a given polygroup P, we construct an Engel fuzzy subgroup μβ*. We obtain a necessary and sufficient condition between Engel fuzzy subpolygroups and the Engel group P/∼, the group of equivalence classes derived from a fuzzy subpolygroup of P. Finally, by using these results, we get Zorn’s lemma, in the Engel fuzzy subpolygroups.

Suggested Citation

  • R. A. Borzooei & E. Mohammadzadeh & Violeta Fotea, 2017. "On Engel Fuzzy Subpolygroups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 195-206, July.
    • Handle: RePEc:wsi:nmncxx:v:13:y:2017:i:02:n:s1793005717500089
    DOI: 10.1142/S1793005717500089
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