CHARACTERIZATIONS OF LINEAR CONGRUENCES ON A FREE MONOID

Linear congruences on a free monoid X coincide with the congruences o n X induced by nontrivial homomorphisms into the additive group of in tegers. For a finite X, we characterize abstractly several classes of linear congruences on X, in particular, pi-linear congruences, called p-linear and determined by Reis, xi-linear congruences, introduced by Petrich and Thierrin, and general linear congruences, introduced by t he authors. These characterizations include descriptions involving max imality as prefix congruences.