Unification


L.P., Unification in varieties of completely simple semigroups, in Contributions to General Algebra 12, Verlag Johannes Heyn, Klagenfurt, 337--348 (2000)

Abstract : We consider solvability of equations with constants in varieties $VCS$ of all completely simple semigroups with subgroups in a given variety $V$ of groups. An equation in $n$ variables and $m$ constants is solvable in $VCS$ if and only if some of a certain system of $m^{2n}$ equations is solvable in $V$. Moreover we discuss the structure of the sets of all solutions. In case $V = AG$ (abelian groups) we find so-called minimal complete sets of solutions.