**Alfred H Clifford** was an American mathematician who worked in group theory and semigroup theory.

- Clifford then went to the California Institute of Technology where he undertook research for a doctorate.
- In 1933 Clifford was awarded his doctorate for his dissertation entitled Arithmetic of Ova.
- After the award of his doctorate, Clifford became a member of the Institute for Advanced Study in Princeton.
- Weyl's influence is clearly seen in Clifford's two papers in 1937 Representations induced in an invariant subgroup.
- Rees's theory generalized much earlier results of Suschkiewitsch unknown to Clifford until 1941.
- Clifford served with distinction for four years, in the European theatre and again in Washington.
- After his period of active duty had ended, Clifford was appointed as an associate professor at Johns Hopkins University.
- However the Korean War saw Clifford return to active duty in 1950 and he served until 1952 when he returned to Johns Hopkins.
- it was at this time that Clifford read J A Green's paper on the structure of semigroups introducing the J, L, R and D relations.
- The influence of this paper on Clifford was immense and quite profound.
- Clifford's 1953 paper 'A class of d-simple semigroups' on d-simple semigroups was his first reaction to Green and was really about inverse d-simple (one D class, and remember Green introduced D) semigroups.
- In 1955 Clifford left Johns Hopkins and moved to New Orleans when he was appointed as Head of Mathematics at Sophie Newcomb College of Tulane University.
- The first volume of Clifford and Preston, The algebraic theory of semigroups, was published in 1961.
- This appeared in the first volume of Semigroup Forum, a mathematics journal which Clifford founded with Hoffman and Mostert in 1970 (it continues to be published by Springer-Verlag).
- In 1974, at the International Congress of Mathematicians in Vancouver, Clifford spoke on orthodox semigroups which are the union of groups.
- In the mid 70's Clifford became very excited by the work of Nambooripad on the structure of regular semigroups in terms of their idempotent ordering and "sandwich matrices" and wrote several expository papers on Nambooripad structure theorem for regular semigroups.
- Clifford's final research, published in 1979, was influenced by universal algebra and concerned determining the structure of the free complexity regular (aka a "union of groups") semigroup on a set.
- After he retired, Clifford left New Orleans and returned to live in California.
- In early December 1992 Clifford suffered a stroke.
- Tulane University had given Clifford a Doctor of Science honoris causa in 1982.

Born 11 July 1908, St Louis, Missouri, USA. Died 27 December 1992, New Orleans, Louisiana, USA.

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Group Theory, Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive