Congruences on free monoids and submonoids of polycyclic monoids
John C. Meakin, Mark Valentinovich Sapir · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1993
Abstract We establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.