Related papers: Specialization of integral dependence for modules
Let $\A$ be an irreducible Coxeter arrangement and $W$ be its Coxeter group. Then $W$ naturally acts on $\A$. A multiplicity $\bfm : \A\rightarrow \Z$ is said to be equivariant when $\bfm$ is constant on each $W$-orbit of $\A$. In this…
The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian Down-Up algebras. We will show that the Noetherian Down-Up algebras A(\alpha,\beta,\gamma) which are fully bounded are…
A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…
Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…
Let R be a polynomial ring over k(u), where k is a field k and u is a finite family or inderterminates. The paper introduces the specialization of an arbitrary finitely generated R-module by the substitution of u to elements of k. This…
Recently the authors investigated the Lipschitz triviality of simple germs of matrices. In this work, we improve some previous results and we present an extension of an integral closure result for the real setting. These tools are applied…
We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…
We study the equisingularity of a family of function germs $\{f_t\colon(X_t,0)\to (\mathbb{C},0)\}$, where $(X_t,0)$ are $d$-dimensional isolated determinantal singularities. We define the $(d-1)$th polar multiplicity of the fibers $X_t\cap…
In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals…
We develop a theory of Hilbert $\widetilde{\C}$-modules by investigating their structural and functional analytic properties. Particular attention is given to finitely generated submodules, projection operators, representation theorems for…
The notions of Betti numbers and of Bass numbers of a finite module N over a local ring R are extended to modules that are only assumed to be finite over S, for some local homomorphism f: R --> S. Various techniques are developed to study…
Let $A\subseteq B$ be a commutative ring extension. Let $\mathcal I(A, B)$ be the multiplicative group of invertible $A$-submodules of $B$. In this article, we extend a result of Sadhu and Singh by finding a necessary and sufficient…
We study modules over a generalized Weyl algebra $R(\sigma,a)$ which are free when restricted to the base ring $R$. When $R$ is an integral domain, we construct all such finite-rank modules up to isomorphism, leading to new simple modules…
We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-modules (namely the local degree and regularity, together with the stable…
This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into complex compact manifolds with applications in global singularity…
We introduce a new numerical invariant $\gamma_I(M)$ associated to a finite-length $R$-module $M$ and an ideal $I$ in an Artinian local ring $R$. This invariant measures the ratio between $\lambda(IM)$ and $\lambda(M/IM)$. We establish…
Generalized Heisenberg algebras $\H(f)$ for any polynomial $f(h)\in\C[h]$ have been used to explain various physical systems and many physical phenomena for the last 20 years. In this paper, we first obtain the center of $\H(f)$, and the…
In this article, we compute the Buchsbaum-Rim function of two variables associated to a direct sum of cyclic modules and give a formula for the last positive associated Buchsbaum-Rim multiplicity in terms of the ordinary Hilbert-Samuel…
This is a largely expository paper, providing a self-contained account on the results of [Sch-Si1, Sch-Si2], in the cases denoted there 2Q and 2M. These papers of Sch\"afke and Singer supplied new proofs to the main theorems of [Bez-Bou,…
For an arbitrary finite dimensional algebra $\Lambda$, we prove that any wide subcategory of $\mathsf{mod} \Lambda$ satisfying a certain finiteness condition is $\theta$-semistable for some stability condition $\theta$. More generally, we…