REPRESENTATIONS AND EMBEDDINGS OF WEAKLY INVERSE SEMIGROUPS (QUASI-STRONG SET)
Abstract
The study of representations of semigroups by transformations of a set was begun in 1952 by Vagner and by Preston 1954 , who showed that any inverse semigroup can be represented by "partial one-to-one mappings". Later, in 1967, Lallement found an analogous result for the broader class of regular semigroups. This thesis includes an analogous result for weakly inverse semigroups (i.e. regular semigroups whose idempotents form a normal band), which gives much more precise information than the work of Yamada 1967 . In 1962, Schein 1962 applied the Vagner-Preston representation theory to construct a universal sub-inverse congruence (i.e. the smallest congruence such that the quotient semigroup is embeddable in an inverse semigroup) on an arbitrary semigroup. This thesis includes a new and simpler proof of Schein's result and also (by making use of the representation theory described above) a corresponding result for embeddings of quotients of an arbitrarily given semigroup into some weakly inverse semigroup.
Degree
Ph.D.
Subject Area
Mathematics
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