For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...

An element f of a commutative ring A with identity element is called a von Neumann regular element if there is a g in A such that fg = f . A point p of a (Tychonoff) space X is called a P -point if each f in the ring C(X) of continuous realvalued functions is constant on a neighborhood of p. It is well-known that the ring C(X) is von Neumann regular ring iff each of its elements is a von Neuman...

A conjecture on vanishing and non-negativity of intersection multiplicity on the blow-up of a regular local ring at its closed point has been proposed. Proofs of vanishing, several special cases of non-negativity and a sufficient condition for non-negativity of this conjecture are described. The topic on intersection multiplicity on vector bundles is also addressed. Introduction. Let X be a reg...

In this paper, we construct an object, called a system of approximate roots of a valuation, centered in a regular local ring, which describes the fine structure of the valuation (namely, its valuation ideals and the graded algebra). We apply this construction to valuations associated to a point of the real spectrum of a regular local ring A. We give two versions of the construction: the first, ...

The purpose of this article is to prove that Gersten’s conjecture for a commutative discrete valuation ring is true. Combining with the result of [GL87], we learn that Gersten’s conjecture is true if the ring is a commutative regular local, smooth over a commutative discrete valuation ring.

In his paper Lyu G Lyubeznik uses the theory of algebraic D modules to study local cohomology modules He proves in particular that if R is any regular ring containing a eld of characteristic zero and I R is an ideal the local cohomology modules H i I R have the following properties i H m H i I R is injective where m is any maximal ideal of R ii inj dimR H i I R dimRH i I R iii The set of the as...

Abstract Given a ring endowed with order, we provide sufficient conditions for the order topology induced by to become (analogous results module orders are consequently derived). Finally, notions of Radon and regular measures transported scope module-valued through orders. Classical characterizations these obtained as well hereditariness regularity conditional ring-valued measures.