Callum Barber

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math.RA2026

Comparing Numbers of Diagonal Subsemigroups and Congruences for Semigroups

Callum Barber, Nik RuÅ¡kuc

Given a semigroup $S$ , a diagonal subsemigroup $I ¨ $ is defined to be a reflexive and compatible relation on $S$ , i.e. a subsemigroup of the direct square $S \times S$ containing the…

math.RA2025

Semigroup Congruences and Subsemigroups of the Direct Square

Callum Barber, Nik RuÅ¡kuc

We investigate semigroups $S$ which have the property that every subsemigroup of $S \times S$ which contains the diagonal ${(s, s) : s \in S}$ is necessarily a congruence on $S…