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TitleMinimal generators for invariant ideals in infinite dimensional polynomial rings
Author(s) Christopher Hillar, Troels Windfeldt
TypeTechnical Report, Misc
AbstractLet K be a field, and let R = K[X] be the polynomial ring in an infinite collection X of indeterminates over K. Let SX be the symmetric group of X. The group SX acts naturally on R, and this in turn gives R the structure of a left module over the group ring R[SX]. 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. As a corollary, we show that there are invariant ideals of R with arbitrarily large minimal Gröbner bases. We also describe minimal Gröbner bases for monomially generated submodules.
Length9
File
LanguageEnglish
Year2006
Translation No
Refereed No
SponsorsRICAM, Special Semester on Groebner Bases 2006
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