Abstract
A usual technique in computational commutative algebra is to reduce the computation of invariants of ideals I⊆ k[ X] where k is a field, to the computation of the corresponding invariant of the monomial ideal M( I) which is associated to I(w.r.t. some term ordering) by means of Gröbner bases, via Buchberger's algorithm. An early instance of this technique is Macaulay's theorem: if I is homogeneous then: dim k ( I n )=dim k ( M( I) n ) for all n. In this paper we give a general version of Macaulay's theorem for ideals in polynomial rings over a noetherian ring R and any additive function λ. As a consequence, the computation of λ( I) for any ideal I can be reduced to the computation of λ( M( I)), for the associated monomial ideal. The result above is obtained by a study of the main properties of Bayer's deformation.
Published Version
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