Partially ordered groups

by Glass, A. M. W., (Andrew Martin William)

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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 au…

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Title Statements

Full title :Partially ordered groups / A.M.W. Glass.

Summary

Edition Statements

Publication Date:1999.

Publication Statements

Publisher(s):World Scientific
Place of Publication:Singapore
Language:eng
Publication Date:1999.

The Physical Object

Description:1 online resource (xiii, 307 pages)

Edition Identifiers

ISBN:9789812816184, 9812816186
oclc:ocn828425184
LC Classification:QA171.485
Dewey Decimal:511.3/2

1. Definitions and examples. 1.1. Right partially ordered groups. 1.2. Partially ordered groups. 1.3. Examples -- 2. Basic properties. 2.1. Basic group-theoretic properties. 2.2. Orderability. 2.3. Basic order-theoretic properties. 2.4. Characterisations of classes -- 3. Values, primes and polars. 3.1. Values. 3.2. Homomorphisms. 3.3. Prime subgroups. 3.4. Special values. 3.5. Polars. 3.6. Closed subgroups. 3.7. A limiting example. 3.8. Residually ordered groups. 3.9. Finite pairwise orthogonal sets -- 4. Abelian and normal-valued lattice-ordered groups. 4.1. Simple Abelian lattice-ordered groups. 4.2. Normal-valued lattice-ordered groups. 4.3. Special-valued lattice-ordered groups. 4.4. Archimedean lattice-ordered groups. 4.5. Hahn's Theorem. 4.6. The Conrad-Harvey-Holland Theorem. 4.7. Elementary theory (Abelian [symbol]-groups) -- 5. Archimedean function groups. 5.1. Free Abelian lattice-ordered groups. 5.2. Finitely presented Abelian [symbol]-groups. 5.3. The isomorphism problem. 5.4. Free products of Abelian [symbol]-groups. 5.5. Kaplansky's example. 5.6. Bernau's Theorem. 5.7. The spectrum. 5.8. Hyperarchimedean [symbol]-groups.

6. Soluble right partially ordered groups & g…