An inequality for Hilbert series of graded algebras.

Hilbert Norms For Graded Algebras

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras included) with respect to which the multiplication is continuous. 2) Such norms cannot be chosen to be submultiplicative and equal to one on the unit of the algeb...

Hilbert Functions of Graded Algebras

Let R be a Noetherian commutative ring with identity, graded by the nonnegative integers N. Thus the additive group of R has a direct-sum decomposition R = R, + R, + ..., where RiRi C R,+j and 1 E R, . I f in addition R, is a field K, so that R is a k-algebra, we will say that R is a G-akebra. The assumption that R is Noetherian implies that a G-algebra is finitely generated (as an algebra over...

Hilbert Functions of Standard Graded Algebras over a Field

In this talk, we introduce Hilbert functions of a graded algebras over a field, and one of the long standing conjectures concerning them, Fröberg conjecture. Then we study relations between Fröberg conjecture on Hilbert series and Moreno-Socias Conjecture. Consequently, we show that Fröberg conjecture holds for special cases as an example. 1. Almost Reverse Lexicographic Monomial Ideal Let R = ...

The Veronese Construction for Formal Power Series and Graded Algebras

Let (an)n≥0 be a sequence of complex numbers such that its generating series satisfies ∑ n≥0 ant n = h(t) (1−t)d for some polynomial h(t). For any r ≥ 1 we study the transformation of the coefficient series of h(t) to that of h〈r〉(t) where ∑ n≥0 anrt n = h 〈r〉(t) (1−t)d . We give a precise description of this transformation and show that under some natural mild hypotheses the roots of h〈r〉(t) c...

An inequality for the hilbert transform.