Abstract

In this paper we sketch the earlier chapters in the history of the mathematical development of the theory of linearly ordered semigroups. The major contributions to the theory occurred in the 1950s and early 1960s, but, as we shall see, these developments were preceded by a scattering of earlier results, which are of broader historical interest with regard to the development of semigroup theory in general.

Introduction

This paper arose as a tribute to A. H. Clifford and significant portions of it were presented at a conference held in his honor on March 28–30, 1994 at Tulane University in New Orleans. Since the authors come from a background of topological semigroups, it seemed appropriate to focus on an aspect of semigroups, namely the theory of linearly ordered semigroups, in which Clifford made significant contributions and which has also impinged on the topological theory. Even though the work of Clifford in this area might not be recognized as the most important or foundational among the varied achievements of this great pioneer of semigroup theory, yet they form an interesting and significant contribution to the development of the theory of linearly ordered semigroups. Clifford wrote a total of five papers [14, 15, 16, 17, 18], all in the 1950s, on the topic of linearly ordered semigroups. One of these, which grew out of a 1957 hour address to the American Mathematical Society, gave a survey of the area as it existed at that time [17] and has proved a helpful reference in the preparation of this article.