Title of article
On the Structure of Order Domains
Author/Authors
Olav Geil، نويسنده , , Ruud Pellikaan، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2002
Pages
28
From page
369
To page
396
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.
Keywords
order domain , Order function , well-orderedsemigroup , valuation theory , Hilbert functions , Gr.obner bases , construction anddecoding of algebraic geometry codes , algorithm of Berlekamp–Massey–Sakata. , order structure
Journal title
Finite Fields and Their Applications
Serial Year
2002
Journal title
Finite Fields and Their Applications
Record number
701054
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