Finite generation of symmetric ideals

  title={Finite generation of symmetric ideals},
  author={Matthias Aschenbrenner and Christopher J. Hillar},
  journal={Transactions of the American Mathematical Society},
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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On well-quasi-ordering transfinite sequences

  • C. Nash-Williams
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1965
Abstract . Let Q be a well-quasi-ordered set, i.e. a set on which a reflexive and transitive relation ≤ is defined and such that, for every infinite sequence q1,q2,… of elements of Q, there exist i

On well-quasi-ordering infinite trees

  • C. Nash-Williams
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1965
Abstract Let A be the set of all ascending finite sequences (with at least one term) of positive integers. Let s, t ∈ A. Write s ⊲ t if there exist m, n, x1, …, xn such that m < n and x1 < … < xn and

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