Keyword: Engel Polygroup : Search

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On Engel Fuzzy Subpolygroups
- R. A. Borzooei,
- E. Mohammadzadeh, and
- Violeta Fotea
New Mathematics and Natural Computation01 Jul 2017
Preview 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 $μ$ $μ$ of $P$ $P$ and $β^{*}$ $β^{*}$ , the fundamental relation on a given polygroup $P$ $P$ , we construct an Engel fuzzy subgroup $μ_{β^{*}}^{*}$ $μ_{β^{*}}$ . We obtain a necessary and sufficient condition between Engel fuzzy subpolygroups and the Engel group $P$ $P$ / $\sim$ $\sim$ , the group of equivalence classes derived from a fuzzy subpolygroup of $P$ $P$ . Finally, by using these results, we get Zorn’s lemma, in the Engel fuzzy subpolygroups.

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