Semigroups - 1st Edition - ISBN: 9780123194503, 9781483267333

Semigroups

1st Edition

Proceedings of the Monash University Conference on Semigroups Held at the Monash University, Clayton, Victoria, Australia, October, 1979

Editors: T. E. Hall P. R. Jones G. B. Preston
eBook ISBN: 9781483267333
Imprint: Academic Press
Published Date: 1st January 1980
Page Count: 266
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Description

Semigroups is a collection of papers dealing with models of classical statistics, sequential computing machine, inverse semi-groups. One paper explains the structure of inverse semigroups that leads to P-semigroups or E-unitary inverse semigroups by utilizing the P-theorem of W.D. Nunn. Other papers explain the characterization of divisibility in the category of sets in terms of images and relations, as well as the universal aspects of completely simple semigroups, including amalgamation, the lattice of varieties, and the Hopf property. Another paper explains finite semigroups which are extensions of congruence-free semigroups, where their set of congruences forms a chain. The paper then shows how to construct such semigroups. A finite semigroup (which is decomposable into a direct product of cyclic semigroups which are not groups) is actually uniquely decomposable. One paper points out when a finite semigroup has such a decomposition, and how its non-group cyclic direct factors, if any, can be found. The collection can prove useful for mathematicians, statisticians, students, and professors of higher mathematics or computer science.

Table of Contents


Contributors

Preface

A Random Ramble through Inverse Semigroups

Divisibility in Categories

Universal Aspects of Completely Simple Semigroups

On the Structure of Regular Semigroups in which the Maximal Subgroups Form a Band of Groups

Interpolation on Semilattices

Constructing Biordered Sets

Semigroups whose Congruences Form a Chain and which are Extensions of Congruence-Free Semigroups

Direct Products of Cyclic Semigroups

Gravity Depth and Homogeneity in Full Transformation Semigroups

The Semigroup of Singular Endomorphisms of a Finite Dimensional Vector Space

Projectives in Some Categories of Semigroups

Generalized Inverse Semigroups and Amalgamation

On Completely Regular Semigroup Varieties and the Amalgamation Property

Embedding Theorems Using Amalgamation Bases

Partially Ordered Semigroups as Semigroups

The Free Elementary * Orthodox Semigroup

On the Regularity of Certain Semigroup Algebras

Semigroups and Graphs

The Formal Structure of Observational Procedures

Details

No. of pages:
266
Language:
English
Copyright:
© Academic Press 1980
Published:
Imprint:
Academic Press
eBook ISBN:
9781483267333

About the Editor

T. E. Hall

P. R. Jones

G. B. Preston