Geodesic
On a connection between fuzzy subgroups and $F$-inverse covers of inverse monoids
Novi Sad Journal of Mathematics, Tome 53 (2023) no. 2.

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We define two categories, the category $\mathfrak{F}\mathfrak{G}$ of fuzzy subgroups, and the category $\mathfrak{F}\mathfrak{C}$ of $F$-inverse covers of inverse monoids, and prove that there is a full and faithful embedding of $\mathfrak{F}\mathfrak{G}$ into $\mathfrak{F}\mathfrak{C}$. As a by-product of this embedding we get that the level subgroups of a given fuzzy subgroup can be realized as the $\mathcal{H}$-classes of a Clifford monoid that is canonically constructed from the fuzzy subgroup. This connection we find between fuzzy subgroups and inverse monoids is new and unexplored before and shows that, at least from a categorical viewpoint, fuzzy subgroups belong to the standard mathematics as much as they do to the fuzzy one.
Publié le :
DOI : 10.30755/NSJOM.12394
Classification : 03E72, 20N25, 20M18
Keywords: fuzzy subgroup, inverse monoid, $F$-inverse cover, dual premorphism 
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Elton Pasku. On a connection between fuzzy subgroups and $F$-inverse covers of inverse monoids. Novi Sad Journal of Mathematics, Tome 53 (2023) no. 2. doi : 10.30755/NSJOM.12394. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.12394/

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