Hilbert Functions of Graded Algebras
نویسنده
چکیده
Let R be a Noetherian commutative ring with identity, graded by the nonnegative integers N. Thus the additive group of R has a direct-sum decomposition R = R, + R, + ..., where RiRi C R,+j and 1 E R, . I f in addition R, is a field K, so that R is a k-algebra, we will say that R is a G-akebra. The assumption that R is Noetherian implies that a G-algebra is finitely generated (as an algebra over k) and that each R, is a finite-dimensional vector space over k. The Hilbe-rt function of R is defined by
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