Variants of epigroups and primary conjugacy
Maria Borralho, Michael Kinyon · Communications in Algebra · 2020
In a semigroup S with fixed c∈S, one can construct a new semigroup (S,·c) called a variant by defining x·cy:=xcy. Elements a,b∈S are primarily conjugate if there exist x,y∈S1 such that a=xy,b=yx. This coincides with the usual conjugacy in groups, but is not transitive in general semigroups. Araújo et al. proved that transitivity holds in a variety W of epigroups containing all completely regular semigroups and their variants, and asked if transitivity holds for all variants of semigroups in W. We answer this affirmatively as part of a study of varieties and variants of epigroups.