On the variety generated by partially ordered involuted semigroups of binary relations (Q2759824)

Consider the class of partially ordered involuted semigroups of binary relations, where the order is the set-theoretical inclusion, involution is the conversion of relations, and multiplication is the relative multiplication. This class generates a variety \(V\) of algebraic systems. Let \(K\) be the class of all partially ordered involuted semigroups and \(K_0=V\cap K\). The main result of the paper is this: a partially ordered involuted semigroup belongs to \(V\) (and hence to \(K_0\)) if and only if it satisfies the identity \(x\leq xx^{-1}x\).NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].