Bounded regularity
نویسنده
چکیده
Let k be a field and S = k[x1, . . . , xn] be a polynomial ring over k. We consider finite sequences of homogeneous polynomials of positive degrees and their operation on non-trivial finitely generated graded S-modules (with grading in Z). Here and in the following, by a polynomial, we always mean an element of S. Moreover, by an S-module we mean in the following a graded S-module with grading in Z. If now M is such a module and additionally Mn = 0 for n ≫ 0, then clearly, there is no regular element on M . It might however be the case that a homogeneous polynomial is regular on M “up to a particular degree”. This motivates of our basic definition:
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