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

1st Edition - January 1, 1980

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  • Editors: T. E. Hall, P. R. Jones, G. B. Preston
  • eBook ISBN: 9781483267333

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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


    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

Product details

  • No. of pages: 266
  • Language: English
  • Copyright: © Academic Press 1980
  • Published: January 1, 1980
  • Imprint: Academic Press
  • eBook ISBN: 9781483267333

About the Editors

T. E. Hall

P. R. Jones

G. B. Preston

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