The Congruence Lattice of Bruck–Reilly Extensions
Brunetto Piochi · Algebra Colloquium · 2000
We study the lattice. C(S) of congruences of a monoid S which is the Bruck-Reilly extension of a monoid T by a homomorphism α. The inclusion, meet and join of congruences are described in terms of congruences and ideals of T . We show that C(S) can be naturally decomposed into three sublattices, corresponding (roughly speaking) to the three different types of congruences on such semigroups.