On Moore families in semigroups

Author

Lawrence William Burns

Date of Award

3-1981

Degree Type

Thesis

Degree Name

Master of Arts

Major

Mathematics

Major Professor

D. D. Miller

Abstract

The properties of Moore families and dual Moore families are studied in general and several specific occurrences of each in semi-groups are shown. In particular, the family of all regular subsets of a semigroup is shown to be a dual Moore family and, based on this fact, the regular core of a subset of a semigroup is defined. The regular core of a Green's class of a semigroup is described and an example is given to show that a J-class J may have a non-empty regular core that is a proper subset of J. The thesis is concluded with a study of congruence relations on a semigroup by use of the properties of Moore families.

Recommended Citation

Burns, Lawrence William, "On Moore families in semigroups. " Master's Thesis, University of Tennessee, 1981.
https://trace.tennessee.edu/utk_gradthes/15146