Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal generators for symmetric ideals


Authors: Christopher J. Hillar and Troels Windfeldt
Journal: Proc. Amer. Math. Soc. 136 (2008), 4135-4137
MSC (2000): Primary 13E05, 13E15, 20B30, 06A07
Published electronically: June 11, 2008
MathSciNet review: 2431024
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13E05, 13E15, 20B30, 06A07

Retrieve articles in all journals with MSC (2000): 13E05, 13E15, 20B30, 06A07


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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09427-6
PII: S 0002-9939(08)09427-6
Keywords: Invariant ideal, symmetric group, Gr\"obner basis, minimal generators
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
Article copyright: © Copyright 2008 American Mathematical Society