Absolute integral closure in positive characteristic

Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke [M. Hochster, C. Huneke, Infinite integral extensions and big Cohen–Macaulay algebras, Ann. of Math. 135 (1992) 53–89] states that if R is excellent, then the absolute integral closure of R is a big Cohen–Macaulay algebra. We prove that if R is the homomorphic image of a Gorenstein local ring, then all the local cohomology (below the dimension) of such a ring maps to zero in a finite extension of the ring. As a result there follow an extension of the original result of Hochster and Huneke to the case in which R is a homomorphic image of a Gorenstein local ring, and a considerably simpler proof of this result in the cases where the assumptions overlap, e.g., for complete Noetherian local domains.     

Actuarial applications of the linear hazard transform in life contingencies

In this paper, we study the linear hazard transform and its applications in life contingencies. Under the linear hazard transform, the survival function of a risk is distorted, which provides a safety margin for pricing insurance products. Combining the assumption of α-power approximation with the linear hazard transform, the net single premium of a continuous life insurance policy can be approximated in terms of the net single premiums of discrete ones. Moreover, Macaulay duration, modified duration and dollar duration, all measuring the sensitivity of the price of a life insurance policy to force of mortality movements under the linear hazard transform, are defined and investigated. Some examples are given for illustration.     

On the Existence of Certain Modules of Finite Gorenstein Homological Dimensions

Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen–Macaulay R-module of finite projective dimension. In this article, we investigate the Gorenstein analogues of these facts.     

Generators and Dimensions of Derived Categories of Modules

Several years ago, Bondal, Rouquier, and Van den Bergh introduced the notion of the dimension of a triangulated category, and Rouquier proved that the bounded derived category of coherent sheaves on a separated scheme of finite type over a perfect field has finite dimension. In this article, we study the dimension of the bounded derived category of finitely generated modules over a commutative Noetherian ring. The main result of this article asserts that it is finite over a complete local ring containing a field with perfect residue field. Our methods also give a ring-theoretic proof of the affine case of Rouquier's theorem.     

Cohen–Macaulayness of Rees Algebras of Modules

Abstract

The notion of quasi-polynomials is very important in the theory of functional identities. For example, results on quasi-polynomials were tools in the solution of long-standing Herstein's Lie map conjectures. In this paper, we show that functional identities involving quasi-polynomial of degree one have only standard solutions on d-free sets.     

A Class of Auslander-Regular Macaulay Rings

Abstract

For a (left and right) noetherian semilocal ring R we analyse a regularity concept (called weak regularity) based on the equation gld R = dim R. Examples are regular Cohen-Macaulay orders over a regular local ring, localized enveloping algebras of finite dimensional Lie algebras, and the regular rings classified in Rump (2001b). We prove that weakly regular rings are Auslander-regular and Macaulay.     

The Edge Ideals of Complete Multipartite Hypergraphs

We classify all complete uniform multipartite hypergraphs with respect to some algebraic properties, such as being (almost) complete intersection, Gorenstein, level, l-Cohen-Macaulay, l-Buchsbaum, unmixed, and satisfying Serre's condition S _r , via some combinatorial terms. Also, we prove that for a complete s-uniform t-partite hypergraph ?, vertex decomposability, shellability, sequentially S _r , and sequentially Cohen–Macaulay properties coincide with the condition that ? has t ? 1 sides consisting of a single vertex. Moreover, we show that the latter condition occurs if and only if it is a chordal hypergraph.     

Generic Initial Ideals of Arithmetically Cohen–Macaulay Projective Subschemes

Supposons qu'un groupe fini G satisfasse l'hypothese suivante: HI Le groupe G opère de manière 2 - transitive sur un ensemble ω |ω|≥3.Soient αβ des élēments distincts de ωH=G_α et D=G_αβ. I1 existe un sous-groupe Q de H tel que H = Q αD.