On the structure of order domains

Olav Geil, Ruud Pellikaan

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Abstract

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, Gröbner algebras, and graded structures is given. The theory of Gröbner 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.
Original languageEnglish
JournalFinite Fields and Their Applications
Volume8
Pages (from-to)369-396
ISSN1071-5797
Publication statusPublished - 2002

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