A special congruence lattice of a regular semigroup.
Mario Petrich · 2007
Abstract. Let S be a regular semigroup and C its lattice of congruences. We consider the sublattice Λ of C generated by σ-the least group, τ-the greatest idem-potent pure, µ-the greatest idempotent separating and β-the least band congruence on S. To this end, we study the following special cases: (1) any three of these congruences generate a distributive lattice, (2) Λ is distributive, (3) the restriction of the K-relation to Λ is a congruence and (4) a further special case. In each of these instances, we provide several characterizations. Our basic concept is that of a c-triple which represents an abstraction of (Λ;K|Λ, T |Λ). 1. Introduction and