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A note on the Hilbert functions of certain ideals which are defined by matrices
Published online by Cambridge University Press: 26 February 2010
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Let I be a homogeneous ideal in the polynomial ring R = Λ[X1, X2, …, XN], where Λ is a field or, more generally, an Artin ring†. Then R|I has an induced structure as a graded R-module and its homogeneous elements of degree n form a Λ-module of finite length. If this length is denoted by H(n, R|I), then H(n, R|I), considered as a function of n, is often known as the Hilbert function of the ideal I although, in other contexts, it is called the Hilbert function of the graded module R|I. We shall adopt the latter terminology.
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