Right (left) inverse semigroups

On sandwich sets and congruences on regular semigroups

“…By ( [11], Theorem 1), a regular semigroup is L-unipotent if and only if it is right regular orthodox. By ( [3], Theorem 2), local L-unipotency is equivalent to both parts (iii) and (iv).…”

The structure of Q⁎-inverse semigroups

“…This class of semigroups not only contains the L * -inverse semigroups as its special subclass but also they can be regarded as an analogue of the quasi-inverse semigroups considered by Yamada in [25] within the class of regular semigroups. Thus, after obtaining the structure of Q * -inverse semigroups, we can establish a corresponding hierarchy between the class of regular semigroups and the class of abundant semigroups, starting from inverse semigroups, left (right) inverse semigroups (see [3] and [23]), quasi-inverse semigroups (see [24]) and orthodox semigroups to type A semigroups, L * -inverse (R * -inverse) semigroups, Q * -inverse semigroups and type W semigroups. In the study of abundant semigroups, one of the most remarkable problems is that a homomorphic image of a regular semigroup is regular but this statement is not true for an abundant semigroup.…”

The structure of ℒ*-inverse semigroups

“…Since the class of the left inverse semigroups is an important subclass of the regular semigroups, its structure and properties have been investigated by many authors, for example, by Bailes [14] , Venkatesan [15] and Yamada [16] . Naturally, one would ask whether we can find an analogue of the left inverse semigroups in the class of abundant semigroups and ask whether we can actually describe the structure of such semigroups?…”