Semigroups

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

T. E. Hall, P. R. Jones, G. B. Preston

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780123194503
• eBook ISBN:
  9781483267333
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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

• Front Cover
• Semigroups
• Copyright Page
• Table of Contents
• CONTRIBUTORS
• PREFACE
• CHAPTER 1. A RANDOM RAMBLE THROUGH INVERSE SEMIGROUPS
• CHAPTER 2. DIVISIBILITY IN CATEGORIES
• CHAPTER 3. UNIVERSAL ASPECTS OF COMPLETELY SIMPLE SEMIGROUPS
• CHAPTER 4. ON THE STRUCTURE OF REGULAR SEMIGROUPS IN WHICH THE MAXIMAL SUBGROUPS FORM A BAND OF GROUPS
• CHAPTER 5. INTERPOLATION ON SEMILATTICES
• CHAPTER 6. CONSTRUCTING BIORDERED SETS
• CHAPTER 7. SEMIGROUPS WHOSE CONGRUENCES FORM A CHAIN AND WHICH ARE EXTENSIONS OF CONGRUENCE-FREE SEMIGROUPS
• CHAPTER 8. DIRECT PRODUCTS OF CYCLIC SEMIGROUPS
• CHAPTER 9. GRAVITY DEPTH AND HOMOGENEITY IN FULL TRANSFORMATION SEMIGROUPS
• CAHPTER 10. THE SEMIGROUP OF SINGULAR ENDOMORPHISMS OF A FINITE DIMENSIONAL VECTOR SPACE
• CHAPTER 11. PROJECTIVES IN SOME CATEGORIES OF SEMIGROUPS
• CHAPTER 12. GENERALIZED INVERSE SEMIGROUPS AND AMALGAMATION
• CHAPTER 13. ON COMPLETELY REGULAR SEMIGROUP VARIETIES AND THE AMALGAMATION PROPERTY
• CHAPTER 14. EMBEDDING THEOREMS USING AMALGAMATION BASES
• CHAPTER 15. PARTIALLY ORDERED SEMIGROUPS AS SEMIGROUPS
• CHAPTER 16. THE FREE ELEMENTARY ORTHODOX SEMIGROUP
• CHAPTER 17. ON THE REGULARITY OF CERTAIN SEMIGROUP ALGEBRAS
• CHAPTER 18. SEMIGROUPS AND GRAPHS
• CHAPTER 19. THE FORMAL STRUCTURE OF OBSERVATIONAL PROCEDURES