Published online by Cambridge University Press: 14 February 2012
In a previous publication [1] we determined the structure of some new types of ordered inverse semigroup in which the ordering need not be the natural ordering. At the moment, very little is known about ordered regular semigroups and the purpose of this paper is to generalise the structure theorems in [1] to corresponding theorems on ordered regular semigroups. The results obtained provide an interesting bridge between the theory of semigroups and that of ordered semigroups, these theories currently having very little in common.