✦ LIBER ✦

On the Structure of Order Domains

✍ Scribed by Olav Geil; Ruud Pellikaan

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 277 KB
Volume: 8
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0347

No coin nor oath required. For personal study only.

✦ Synopsis

The notion of an order domain is generalized. The behaviour of an order domain by taking a subalgebra, the extension of scalars, and the tensor product is studied. The relation of an order domain with valuation theory, Gr .

o obner algebras, and graded structures is given. The theory of Gr .

o obner bases for order domains is developed and used to show that the factor ring theorem and its converse, the presentation theorem, hold. The dimension of an order domain is related to the rank of its value semigroup.

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