An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings

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A \textit{symmetric ideal} $I \subseteq R = K[x_1,x_2,...]$ is an ideal that is invariant under the natural action of the infinite symmetric group. We give an explicit algorithm to find Gröbner bases for symmetric ideals in the infinite dimensional polynomial ring $R$. This allows for symbolic computation in a new class of rings. In particular, we solve the ideal membership problem for symmetric ideals of $R$.
preliminary abstract, 10 pages

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Commutative Algebra, Combinatorics, 13E05, 13E15, 20B30, 06A07

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http://salesiana.dossiersoluciones.com/handle/123456789/146833

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.4439
 http://arxiv.org/abs/0801.4439

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arXiv