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On Engel Fuzzy Subpolygroups

R. A. Borzooei

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

E-mail Address: borzooei@sbu.ac.ir

Corresponding author.

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E. Mohammadzadeh

Department of Mathematics, Faculty of Science, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

E-mail Address: mohammadzadeh.e@pnurazavi.ac.ir

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, and

Violeta Fotea

Faculty of Mathematics, Alexandru Ioan Cuza University, 700506 Iasi, Romania

E-mail Address: foteavioleta@gmail.com

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https://doi.org/10.1142/S1793005717500089Cited by:5 (Source: Crossref)

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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References

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On Engel Fuzzy Subpolygroups

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