$F$-congruences on $F$-inverse monoids

Ajda Lemut Furlani

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arXiv · 2608.15114

$F$-congruences on $F$-inverse monoids

Ajda Lemut Furlani

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Abstract

We study the class of congruences on $F$-inverse monoids that respect the unary operation $a\mapsto\mx{a}$, assigning to each element the maximum element of its $σ$-class, which we refer to as $F$-congruences. We characterize kernel normal systems and congruence pairs on $F$-inverse monoids which give rise to such congruences and establish a number of further related results including a classification of $F$-congruence-free $F$-inverse monoids.

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Ajda Lemut Furlani. 2026-08-15. $F$-congruences on $F$-inverse monoids. https://arxiv.org/abs/2608.15114

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