Sobre a existencia de bases SAGBI finitas para o nucleo de k-derivações em k[x1,...,xn] / About the existence of finite SAGBI bases for the kernel of a k-derivation in k[x1,...,xn]

AUTOR(ES)

Angelo Calil Bianchi

DATA DE PUBLICAÇÃO

2008

RESUMO

The general objective of this work is to understand the SAGBI bases theory from a structural point of view, seeking criterias for it’s existence and results that prove it’s effitiency in the study of certain subalgebras of k[x], as well as to study the general theory of derivations over polynomial rings, it’s localizations and quotients, in order to explore the algebraic properties of the kernel of this derivations and the structures of the k-subalgebras of k[x] that may be seen as such kernels. The specific objective is to study the algebraic-geometric theory of k-derivations in k[x], developed by Shigeru Kuroda, and to use this theory to stabilish a condition for the kernel of one such derivation to be a finitely generated k-subalgebra and another condition for this derivation to have finite SAGBI base. Along this work we also want to emphasize the behavior of locally nilpotent k-derivations and to obtain an algorithmic way to determine the generators of it’s kernels, in the particular case that the derivation has a slice.

ASSUNTO(S)

bases differential algebra sagbi bases algebra comutativa commutative algebra sagbi algebra diferencial

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