Reidemeister- Schreier type rewriting for semigroups.
Completely regular semigroups are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes a variety; its lattice of subvarieties is denoted by . We study here the relations and relative to a sublattice of constructed in a previous publication. For being any of these relations, we determine the -classes of all varieties in the lattice as well as the restrictions of to .
We introduce relative block semigroups as an appropriate tool for the study of certain phenomena of non-unique factorizations in residue classes. Thereby the main interest lies in rings of integers of algebraic number fields, where certain asymptotic results are obtained.