The relation \(\mathcal B\) in \(le\)-semigroups (Q2461624)

The main goal of this paper is to study a relation (denoted by \(B\)) in an le-semigroup, which is similar with the relation ``to generate the same bi-ideal'' in the plain semigroup case. In general, it is finer than the Green-Kehayopulu relation \(H\) studied in the previous paper [ibid. 65, 33--42 (2002; Zbl 1003.06008)] by the same authors and, consequently, it has better properties. In Section 2 some necessary and sufficient conditions for a \(B\)-class to be regular or intra-regular are indicated. Section 3 deals with the case in which a \(B\)-class is a subsemigroup. A remarkable characterization of these classes is given by Theorem 3.1.