Partial kernel normal systems in regular semigroups. (English) Zbl 1002.20037

He, Yong

Semigroup Forum 64, No. 2, 325-328 (2002).

Let \(S\) be a regular semigroup and \(E\) its set of idempotents. A subset \(P\) of \(E\) is called full if it meets every \(\mathcal L\)-class and every \(\mathcal R\)-class. If \(\rho\) is a congruence on \(S\) and \(P\) a full subset of \(E\), then the set of \(\rho\)-classes each of which containing at least one idempotent of \(P\) is called the partial kernel normal system of \(\rho\) linked to \(P\). It is proved that \(\rho\) is uniquely determined by its partial kernel normal system linked to \(P\), and an abstract characterization of such partial kernel normal systems is given.

Reviewer: F.J.Pastijn (Milwaukee)

MSC:

20M17

Regular semigroups

Keywords:

regular semigroups; idempotents; congruences; partial kernel normal systems