A Study of Regular Grouplikes

Abstract

Recently, a new algebraic structure, namely grouplike, has
been introduced and studied by the first author. A grouplike is something
between semigroup and group with so close relations to groups.
The grouplike axioms are generalizations of the four group axioms. In
this paper, we study regular and irregular grouplikes as a class of semigroups.
The motivation of this study lies in some interesting properties
of regular proper grouplikes.