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.References
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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