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Partially Ordered Algebraic Systems (Dover Books on Mathematics), by Laszlo Fuchs, Mathematics
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Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields.
The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap in many individual and institutional libraries.
- Sales Rank: #2702989 in Books
- Brand: Fuchs, Laszlo
- Published on: 2011-11-17
- Released on: 2011-10-20
- Original language: English
- Number of items: 1
- Dimensions: 8.40" h x .80" w x 5.30" l, .55 pounds
- Binding: Paperback
- 238 pages
About the Author
Fuchs is a W.R. IRBY Professor of Mathematics at Tulane University, New Orleans, Louisiana.
Most helpful customer reviews
5 of 5 people found the following review helpful.
Very useful and very well written.
By Alan U. Kennington
This 1963 book is much more useful than I had expected. The subject area is broader than the title suggests. I've found it immediately useful for Archimedean totally ordered groups and rings for example.
The subject of general ordered algebraic systems is not much written about, in my experience so far anyway. And yet this book, "Partially Ordered Algebraic Systems" goes beyond total order to general partial orders (particularly lattices) on algebraic systems including groups, rings, fields and even semigroups! When I ordered the book, I was not optimistic that it would be useful. But the first thing I looked up was fully covered with all of the information that I wanted. Specifically, that was H�lder's theorem for Archimedean totally ordered groups, pages 45-46. (The author calls totally ordered sets "fully ordered".) There's a full, clear proof of this theorem, plus the motivation, context and applications. (I immediately added the reference to the wikipedia article on this subject.)
The topic coverage of this book is clearly visible in the Amazon preview. So I don't need to tell you what it covers. I will just say that I'm very happy with it, it fills a significant gap in my collection of algebra textbooks, it's well bound and well printed, and well written. I wish all algebra books were so clearly written. This subject area of algebra is not covered (apart from extremely brief peripheral mentions) in the big standard algebra textbooks by Mac Lane and Birkhoff, and by Serge Lang, for example.
It is quite intriguing how order interacts with algebraic structures. Order puts quite strong constraints on the properties of addition and multiplication operations. The H�lder theorem is just one example of this.
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