Details:
Title  Minimal generators for invariant ideals in infinite dimensional polynomial rings  Author(s)  Christopher Hillar, Troels Windfeldt  Type  Technical Report, Misc  Abstract  Let 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.  Length  9 
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 Language  English  Year  2006  Translation 
No  Refereed 
No  Sponsors  RICAM, Special Semester on Groebner Bases 2006 
