On E-unitary regular semigroups (Q1862918)

The structure of E-unitary regular semigroups is described in terms of so-called PO-sextets. The first three ingredients of the sextet, \((G,X,Y)\), form a McAlister triple as in the theory of E-unitary inverse semigroups. The fourth is a set \(P\) which is a union of sets \(P_\alpha\) (\(\alpha\in Y\)) while the fifth and sixth are certain collections of mappings defined on certain direct products of factor sets of the \(P_\alpha\). A parallel theory is developed for the class of E-unitary weak regular *-semigroups.