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Minimal generators for invariant ideals in infinite dimensional polynomial rings (2006).
| Content Provider | CiteSeerX |
|---|---|
| Author | Hillar, Christopher J. Windfeldt, Troels |
| Abstract | 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. 1. |
| File Format | |
| Publisher Date | 2006-01-01 |
| Access Restriction | Open |
| Subject Keyword | Polynomial Ring Infinite Collection Invariant Ideal Recent Theorem Large Minimal Gr Bner Base Left Module Hillar State Minimal Generator Minimal Gr Bner Base Symmetric Group Group Sx |
| Content Type | Text |
| Resource Type | Article |
