Sobre derivações localmente nilpotentes dos aneis K[x,y,z] e K[x,y] / Over locally nilpotent derivations of the rings K[x,y,z] e K[x,y]

AUTOR(ES)

Maribel del Carmen Diaz Noguera

DATA DE PUBLICAÇÃO

2007

RESUMO

In this dissertation we present centraIs results on locally nilpotents derivations in a ring of polynomials B = k[x1, ..., xn], for n ≤ 3, which were presented by Daniel Daigle in [2], [3] and [4]. For this, we introduce basic fundamenta1 results of the theory of derivations in a ring and we present results on locally nilpotents derivations in a domain with characteristic zero and unique factorization. One of these results is the Jacobian forrnula that we use to describe the set of the equivalent loca11y nilpotents derivations of B = k[x, y, z] and the set LND(B) where B = k[x, y]. Moreover, we give equivalent conditions to the existence of a ω-homogeneous locally nilpotent derivation in the ring B = k[x, y, z] with kernel k[ƒ, g], {ƒ} and {g} ε B, and mdc(ω) = mdc(ω(ƒ), ω (g)) = 1.

ASSUNTO(S)

algebra aneis polinomiais polynomial rings algebra comutativa algebra commutative algebra

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