On the Structure of Order Domains

Authors:
Olav Geil;Ruud Pellikaan
Affiliations:
Department of Mathematics, Aalborg University, Frederik Bajersvej 7G, DK9220, Aalborg ø Denmark;Department of Mathematics and Computing Science, Technical University of Eindhoven, 513, 5600, MB, Eindhoven, The Netherlands
Venue:
Finite Fields and Their Applications
Year:
2002

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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, Grobner algebras, and graded structures is given. The theory of Grobner 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.