Congruences on regular semigroups

Pachaury, Vijaykar (1967) Congruences on regular semigroups. MSc(R) thesis, University of Glasgow.

Abstract

It is well known that the set of congruences on a semigroup (or indeed on any Algebra) forms a lattice if ordered by set-theoretic inclusion. In this thesis certain results are presented about congruences on regular semigroups with particular emphasis on lattice-theoretic properties of the lattice of congruences. Chapter I is of an introductory natures in which we summarise some basic results in the theory of semigroups. In Chapter II, certain special congruences on a regular semigroup are considered, such as the minimum group, band and semilattice congruences and the maximum idempotent-separating congruences. Inter-relations among these congruences and their mutual intersections and joins are also examined. The special case of inverse semigroup is considered at the end of the chapter. Most of the material presented in this chapter is due to Howie and Howie and Lallement. Chapter III is devoted to an account of the recent work of Munn, Reilly and Munn and Reilly on congruences on bisimple w-semigroups. In Chapter IV an account is given of Tamura's characterization of congruences on completely 0-simple semigroups. This characterization is used to give a new proof of the semi-modularity of the lattice of congruences in a completely 0-simple semigroup, a result due in the first instance to Lallement.

• Item Type: Thesis (MSc(R))
• Qualification Level: Masters
• Additional Information: Adviser: R A Rankin
• Keywords: Mathematics
• Date of Award: 1967
• Depositing User: Enlighten Team
• Unique ID: glathesis:1967-72198
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 24 May 2019 15:11
• Last Modified: 24 May 2019 15:11
• URI: https://theses.gla.ac.uk/id/eprint/72198