An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings

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dc.creatorAschenbrenner, Matthias
dc.creatorHillar, Christopher J.
dc.date2008-01-29
dc.date.accessioned2026-07-07T08:57:04Z
dc.date.available2026-07-07T08:57:04Z
dc.descriptionA \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 $R$.
dc.descriptionpreliminary abstract, 10 pages
dc.identifierhttps://arxiv.org/abs/0801.4439
dc.identifierhttp://arxiv.org/abs/0801.4439
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146833
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13E05, 13E15, 20B30, 06A07
dc.titleAn Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Rings
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