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Noether whole ring compound Groebner bases

Author: TangSheng
Tutor: ChenXiaoSong
School: Central South University
Course: Computational Mathematics
Keywords: Complex Noether whole ring Groebner Bases Syzygy conditions S-polynomial
CLC: O153.3
Type: Master's thesis
Year: 2008
Downloads: 15
Quote: 0
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Abstract


Composite means of the polynomial for each of a variable element with a new polynomial substitution . First of all, the formation of the theory of Groebner bases , research background and composite Groebner bases theory , the basics of the theory of Groebner bases and knowledge of algebra . Secondly , the introduction of the scholars on the nature of the polynomial composite Groebner bases , the Groebner bases composite and domain homogeneous composite , weighted Sarkozy times composite exchange and domain irreducible complex Groebner bases made details . In this paper, by introducing the S- polynomial syzygy conditions are given and proved a the Groebner base in the polynomial ring of n Arguments in the on Noether whole ring calculated with m (m ≥ n) number of Arguments - ring composite a Sufficient conditions : composite term order two different polynomial ring , compatibility and is a product of the product from the first power of the rest of the arguments for the arrangement of power and arrangement power plot the first polynomial . Which the calculation of the minimal Groebner bases composite exchangeable . In particular , if the composite is a group of the first power compatible with the term order plot for the arrangement of the power of the first polynomial calculation of Groebner base and composite exchangeable . Given and proved for the different nature of the entry sequence , Noether integral ring A Sufficient conditions for the calculation of Groebner bases in a sequence with another sequence composite : composite first power plot is arranged the power of a polynomial .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Ring Theory
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