Partial kernel normal systems for eventually regular semigroups. (English) Zbl 1098.20046

Shao, Fang; He, Yong

Semigroup Forum 71, No. 3, 401-410 (2005).

A semigroup \(S\) is eventually regular (sometimes \(\pi\)-regular elsewhere in the literature) if some power of each element is regular. The authors have generalised the familiar notion of kernel normal system to that of a so-called \(P\)-partial kernel normal system and prove that every regular congruence on \(S\) is uniquely determined by its \(P\)-partial kernel normal system. The set of \(P\)-partial kernel normal systems of \(S\) forms a complete lattice that is a meet-homomorphic image of the lattice of congruences of \(S\).

Reviewer: Peter M. Higgins (Colchester)

MSC:

20M17	Regular semigroups
08A30	Subalgebras, congruence relations

Keywords:

partial kernel normal systems; eventually regular semigroups; lattices of congruences; regular congruences