# Finite generation of symmetric ideals

@article{Aschenbrenner2004FiniteGO, title={Finite generation of symmetric ideals}, author={Matthias Aschenbrenner and Christopher J. Hillar}, journal={Transactions of the American Mathematical Society}, year={2004}, volume={359}, pages={5171-5192} }

Let be a commutative Noetherian ring, and let be the polynomial ring in an infinite collection of indeterminates over . Let be the group of permutations of . The group acts on in a natural way, and this in turn gives the structure of a left module over the group ring . We prove that all ideals of invariant under the action of are finitely generated as -modules. The proof involves introducing a certain well-quasi-ordering on monomials and developing a theory of Grobner bases and reduction in…

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