Hilbert series and applications to graded rings
نویسندگان
چکیده
منابع مشابه
Ideal bases for graded polynomial rings and applications to interpolation
Based on a generalized algorithm for the division with remainder of polynomials in several variables, a method for the construction of standard bases for polynomial ideals with respect to arbitrary grading structures is derived. In the case of ideals with finite codimension, which can be viewed upon as a polynomial interpolation problem, an explicit representation for the interpolation space of...
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Given a local Cohen-Macaulay ring (R,m), we study the interplay between the integral closedness – or even the normality – of an m-primary R-ideal I and conditions on the Hilbert coefficients of I . We relate these properties to the depth of the associated graded ring of I .
متن کاملComputing Hilbert–kunz Functions of 1-dimensional Graded Rings
According to a theorem of Monsky, the Hilbert–Kunz function of a 1-dimensional standard graded algebra R over a finite field K has, for i 0, the shape HKR(i) = c(R) · p i + φ(i), where c(R) is the multiplicity of R and φ is a periodic function. Here we study explicit computer algebra algorithms for computing such Hilbert–Kunz functions: the period length and the values of φ, as well as a concre...
متن کاملSets of Hilbert Series and Their Applications
We consider graded finitely presented algebras and modules over a field. Under some restrictions, the set of Hilbert series of such algebras (or modules) becomes finite. Claims of that types imply rationality of Hilbert and Poincare series of some algebras and modules, including periodicity of Hilbert functions of common (e.g., Noetherian) modules and algebras of linear growth.
متن کاملGraded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203107090