Bounds in Polynomial Rings over Artinian Local Rings
نویسنده
چکیده
Let R be a (mixed characteristic) Artinian local ring of length l and let X be an n-tuple of variables. This paper provides bounds over the ring R[X] on the degrees of the output of several algebraic constructions in terms of l, n and the degrees of the input. For instance, if I is an ideal in R[X] generated by polynomials gi of degree at most d and if f is a polynomial of degree at most d belonging to I , then f = q1f1 + · · · + qsfs, with qi of degree bounded in terms of d, l and n only. Similarly, the module of syzygies of I is generated by tuples all of whose entries have degree bounded in terms of d, l and n only.
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