Semigroup Theory and Its Applications: Proceedings of the 1994 Conference Commemorating the Work of Alfred H. CliffordThis volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable. |
Contents
A H Cliffords work on unions of groups | 5 |
A survey on totally ordered semigroups | 15 |
The relationship of Al Cliffords work to the current theory of semigroups | 43 |
variations on a Clifford Theme | 53 |
Isbells zigzag theorem and its consequences | 81 |
Maps implicit in the JordanHolder theorem | 95 |
Finite semigroups as categories ordered semigroups or compact semigroups | 107 |
Principles underlying the degeneracy of models of the untyped lambda calculus | 123 |
Special involutions | 157 |
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Common terms and phrases
algebraic archimedean band of monoids bicyclic semigroup bijective called cartesian closed category Clifford semilattice commutative semigroups compact components composition series construction Corollary defined Definition denote direct product epimorphism equivalent example finite monoids finite semigroups function functor Hausdorff hence Hofmann HÖLDER homomorphisms I-semigroups ideal idempotents implies interval inverse semigroup invertible elements involution isomorphism Jordan-Hölder theorem lambda calculus languages lattice left zero Lemma linearly ordered semigroup Math Mathematical matrix morphism multiplication naturally totally ordered object ordered set ordinal sum ordinally irreducible paper phism pr₁ profinite Proof proper band pseudovarieties quasi order quotient rectangular band regular semigroups representation sandwich satisfies semi semigroup theory semilattice sequence simple semigroups special involution spined product stratified E-band subgroups submonoid subsemigroup Suppose surjective system of homomorphisms topological semigroup totally ordered transitive system unions of groups variety of finite