ON HILBERT SERIES FOR COMMUTATIVE AND NONCOMMUTATIVE GRADED ALGEBRAS

[摘要] Let d1,...,d(r) be positive integers. We show that there are only finitely many Hilbert functions for rings k[X1,...,X(n)]/(f1,...,f(r)), where f(i) is a form of degree d(i). Furthermore, there is a Zariski-open dense subset of the space of coefficients of the forms, where the Hilbert functions are equal. Both these statements are false in the noncommutative case.

[发布日期] 1991-11-25