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Let $R$ be a polynomial ring over a field and $M= bigoplus_n M_n$ a finitely generated graded $R$-module, minimally generated by homogeneous elements of degree zero with a graded $R$-minimal free resolution $mathbf{F}$. A Cohen-Macaulay module $M$ is Gorenstein when the graded resolution is symmetric. We give an upper bound for the first Hilbert coefficient, $e_1$ in terms of the shifts in the graded resolution of $M$. When $M = R/I$, a Gorenstein algebra, this bound agrees with the bound obtained in cite{ES} in Gorenstein algebras with quasi-pure resolution. We conjecture a similar bound for the higher coefficients.
We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-Soderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of rational multiples
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t,t^{-1}]-module associated to R. This module, denoted J(R), is the free Z[t,t
Let fa be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Let cd_{fa}(M,N) denote the supremum of the is such that H^i_{fa}(M,N) eq 0. First, by using the theory of Gorenstein homological dimensions, we obtai
In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area of dynamic
We prove that, analogous to the HK density function, (used for studying the Hilbert-Kunz multiplicity, the leading coefficient of the HK function), there exists a $beta$-density function $g_{R, {bf m}}:[0,infty)longrightarrow {mathbb R}$, where $(R,