Hilbert polynomials over Artinian rings (Q1300135)

A standard algebra over a commutative Artinian ring \(R_{0}\) is a graded ring \(S\) that is finitely generated as \(R_{0}=S_{0}\)-algebra by elements of degree one. The authors characterize the Hilbert functions and Hilbert polynomials of such algebras, thereby continuing a program begun by \textit{F. S. Macaulay} [Proc. Lond. Math. Soc., II. Ser. 26, 531-555 (1927; JFM 53.0104.01)]. Results of \textit{G. Gotzmann} [Math. Z. 158, 61-70 (1978; Zbl 0352.13009)] are suitably extended.