A class of Hilbert series and the strong Lefschetz property
نویسندگان
چکیده
منابع مشابه
A Class of Hilbert Series and the Strong Lefschetz Property
We determine the class of Hilbert series H so that if M is a finitely generated zero-dimensional R-graded module with the strong Lefschetz property, then M ⊗k k[y]/(y ) has the strong Lefschetz property for y an indeterminate and all positive integers m if and only if the Hilbert series of M is in H. Given two finite graded R-modules M and N with the strong Lefschetz property, we determine suff...
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Stanley [4] showed that monomial complete intersections have the strong Lefschetz property. Extending this result we show that a simple extension of an Artinian Gorenstein algebra with the strong Lefschetz property has again the strong Lefschetz property. Introduction Let K be a field, A be a standard graded Artinian K-algebra and a ∈ A a homogeneous form of degree k. The element a is called a ...
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The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in [Wi]) whose Gotzmann ideals have the WLP. This implies that, if a Gotzmann ideal has the WLP, then all algebras with the same Hilbert function (and hence lower Betti...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10498-7