Series in Algebra - Vol. 7
PARTIALLY ORDERED GROUPS
by A M W Glass (University of Cambridge, England/Professor Emeritus, Bowling Green State University, Ohio)
Recently the theory of partially ordered groups has been used by analysts, algebraists, topologists and model theorists. This book presents the most important results and topics in the theory with proofs that rely on (and interplay with) other areas of mathematics. It concludes with a list of some unsolved problems for the reader to tackle. In stressing both the special techniques of the discipline and the overlap with other areas of pure mathematics, the book should be of interest to a wide audience in diverse areas of mathematics.
Contents:
- Definitions and Examples
- Basic Properties
- Values, Primes
and Polars
- Abelian and Normal-Valued Lattice-Ordered Groups
- Archimedean Function Groups
- Soluble Right Partially Ordered Groups and Generalisations
- Permutations
- Applications
- Completions
- Varieties of Lattice-Ordered Groups
- Unsolved Problems
Readership: Pure mathematicians.
"The author's style of writing is very lucid, and the material presented is self-contained. It is an excellent reference text for a graduate course in this area, as well as a source of material for individual reading."
| Bulletin of London Mathematical Society |
"This monograph is clearly written, well organized ... can be warmly recommended to students and research workers dealing with the theory of partially ordered groups."
"Glass's book will get the reader to the forefront of research in the field and would be a suitable text for students in modern algebra, group theory, or ordered structures. It will surely find its place in all mathematical libraries and on the desks of the professional algebraists and 'ordered- groupers'."
| 324pp |
Pub. date: Jul 1999 |
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