In this note the Briançon-Skoda theorem is extended to Noetherian filtrations of ideals in a regular ring. The method of proof couples the Lipman-Sathaye approach with results due to Rees. Let A be a regular ring of dimension d and I an ideal of A. Let I denote the integral closure of I. The Briançon-Skoda theorem asserts that if I is generated by l elements then In+l ⊆ I, for all nonnegative i...

Given a standard graded polynomial ring over commutative Noetherian $A$, we prove that the cohomological dimension and height of ideals defining any its Veronese subrings are equal. This result is due to Ogus when $A$ field characteristic zero, follows from Peskine Szpiro positive characteristic; our applies, for example, integers.

let $r$ be a commutative noetherian ring with non-zero identity and $fa$ an ideal of $r$. let $m$ be a finite $r$--module of finite projective dimension and $n$ an arbitrary finite $r$--module. we characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(m,n)$ in certain serre subcategories of the category of modules from upper bounds. we define and study the properti...

We show that many noetherian Hopf algebras A have a rigid dualising complex R with R = A[d]. Here, d is the injective dimension of the algebra and ν is a certain k-algebra automorphism of A, unique up to an inner automorphism. In honour of the finite dimensional theory which is hereby generalised we call ν the Nakayama automorphism of A. We prove that ν = Sξ, where S is the antipode of A and ξ ...

We show that, for a pseudo-proper smooth noetherian formal scheme $\mathfrak{X}$ over positive characteristic $p$ field, its truncated De Rham complex up to the is decomposable. Moreover, if dimension of exactly $p$, then full Along way we establish Cartier isomorphism associated morphism schemes.

The Macaulayfication of a Noetherian scheme X is a birational proper morphism Y → X such that Y is a CohenMacaulay scheme. Of course, a desingularization is a Macaulayfication and Hironaka gave a desingularization of arbitrary algebraic variety over a field of characteristic 0. In 1978 Faltings gave a Macaulayfication of a quasi-projective scheme whose nonCohen-Macaulay locus is of dimension 0 ...