STRUCTURE OF RELATIVELY FREE BANDS
Mario Petrich, Pedro V. Silva · Communications in Algebra · 2002
Based on the operators and and their duals and defined on the free semigroup for a nonempty set by Gerhard and Petrich, we introduce here the operators which are proved to be homomorphisms of onto certain subsets of with suitable multiplication. These operators induce fully invariant congruences on corresponding to most of the varieties of bands if X is countably infinite. Variants of operators and introduced by the cited authors are used here to elucidate the structure of relatively free bands for most band varieties in conjunction with the operators . The few remaining varieties are treated separately.