相关论文: Hilbert series of modules over Lie algebroids

We state criteria for a nilpotent Lie algebra $\g$ to admit an invariant metric. We use that $\g$ possesses two canonical abelian ideals $\ide(\g) \subset \mathfrak{J}(\g)$ to decompose the underlying vector space of $\g$ and then we state…

We provide the definition and fundamental properties of algebraic elements with respect to an operator satisfying hypothesis (h). Furthermore, we analyze Hilbert modules using C_0-operators relative to a bounded finitely connected region…

Let $\cl{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\mathcal{A}(\Omega)$, where $\Omega \subseteq \bb{C}^m$ is a bounded domain. Let $\cl{M}_0\subseteq \cl{M}$ be the submodule of functions vanishing…

We characterize the class of ideals of a polynomial ring such that the hilbert series of their graded local cohomology modules is maximal.

The purpose of the present paper is to prove some properties of the strongly irreducible submodules in the arithmetical and Noetherian modules over a commutative ring. The relationship among the families of strongly irreducible submodules,…

We introduce and study a notion of Serre liftable modules; these are modules that are liftable to modules of the maximal possible dimension over a regular local ring. We establish new cases of Serre's positivity conjecture over ramified…

Let $(A,\mathfrak{m})$ be a hypersurface local ring of dimension $d \geq 1$, $N$ a perfect $A$-module and let $I$ be an ideal in $A$ with $\ell(N/IN)$ finite. We show that there is a integer $r_I \geq -1$ (depending only on $I$ and $N$)…

Let $X=(x_{ij})$ and $Y=(y_{ij})$ be generic $n$ by $n$ matrices and $Z=XY-YX$. Let $S=k[x_{11},...,x_{nn},y_{11},...,y_{nn}]$, where $k$ is a field, let $I$ be the ideal generated by the entries of $Z$ and let $R=S/I$. We give a conjecture…

Over a regular local ring of dimension two with maximal ideal m, we study the Buchsbaum-Rim multiplicity of a finitely generated module M of finite colength in a free module F. First, we investigate the colength of an m-primary ideal and…

Let $J\subset S=K[x_0,...,x_n]$ be a monomial strongly stable ideal. The collection $\Mf(J)$ of the homogeneous polynomial ideals $I$, such that the monomials outside $J$ form a $K$-vector basis of $S/I$, is called a {\em $J$-marked…

We consider modules E over a C*-algebra A which are equipped with a map into A_+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, we show that if A has no nonzero commutative…

For any open, connected and bounded set $\Omega \subseteq \mathbb C^m$, let $\mathcal A$ be a natural function algebra consisting of functions holomorphic on $\Omega$. Let $\mathcal M$ be a Hilbert module over the algebra $\mathcal A$ and…

It is well known that the ring radical theory can be approached via language of modules. In this work, we present some generalizations of classical results from module theory, in the two-sided and graded sense. Let $\mathsf{G}$ be a group,…

We study the Hilbert series of a family of ideals J_\phi generated by powers of linear forms in k[x_1,...,x_n]. Using the results of Emsalem-Iarrobino, we formulate this as a question about fatpoints in P^{n-1}. In the three variable case…

We fix the lexicographic order $\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define $\Hi^{\prec\Delta}_{S/k}$, the moduli space of reduced Gr\"obner bases with a given finite standard set $\Delta$, and its open…

It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the…

The acquisition of the defining equations of Rees algebras is a natural way to study these algebras and allows certain invariants and properties to be deduced. In this paper, we consider Rees algebras of codimension 2 perfect ideals of…

For $K$ a field, consider a finite subgroup $G$ of $\operatorname{GL}_n(K)$ with its natural action on the polynomial ring $R:=K[x_1,\dots,x_n]$. Let $\mathfrak{n}$ denote the homogeneous maximal ideal of the ring of invariants $R^G$. We…

Let $M$ be a finitely generated module over a Noetherian local ring. This paper reports, for a given parameter ideal $Q$ for $M$, a criterion for the equality…

The growth of Hilbert coefficients for powers of ideals are studied. For a graded ideal $I$ in the polynomial ring $S=K[x_1,...,x_n]$ and a finitely generated graded $S$-module, the Hilbert coefficients $e_i(M/I^kM)$ are polynomial…