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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal generators for symmetric ideals
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by Christopher J. Hillar and Troels Windfeldt PDF
Proc. Amer. Math. Soc. 136 (2008), 4135-4137 Request permission

Abstract:

Let $R = K[X]$ be the polynomial ring in infinitely many indeterminates $X$ over a field $K$, and let ${\mathfrak S}_{X}$ be the symmetric group of $X$. The group ${\mathfrak S}_{X}$ acts naturally on $R$, and this in turn gives $R$ the structure of a module over the group ring $R[{\mathfrak S}_{X}]$. A recent theorem of Aschenbrenner and Hillar states that the module $R$ is Noetherian. We address whether submodules of $R$ can have any number of minimal generators, answering this question positively.
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Additional Information
  • Christopher J. Hillar
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email: chillar@math.tamu.edu
  • Troels Windfeldt
  • Affiliation: Department of Mathematical Sciences, University of Copenhagen, DK-1165 Copenhagen, Denmark
  • Email: windfeldt@math.ku.dk
  • Received by editor(s): September 6, 2006
  • Received by editor(s) in revised form: October 25, 2007
  • Published electronically: June 11, 2008
  • Additional Notes: The work of the first author was supported under an NSF Postdoctoral Fellowship.
  • Communicated by: Bernd Ulrich
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 4135-4137
  • MSC (2000): Primary 13E05, 13E15, 20B30, 06A07
  • DOI: https://doi.org/10.1090/S0002-9939-08-09427-6
  • MathSciNet review: 2431024