Anti-integral extensions $ {R[{\alpha}]/R$

Codimension, Multiplicity and Integral Extensions

Let A ⊂ B be a homogeneous inclusion of standard graded algebras with A0 = B0. To relate properties of A and B we intermediate with another algebra, the associated graded ring G = grA1B(B). We give criteria as to when the extension A ⊂ B is integral or birational in terms of the codimension of certain modules associated to G. We also introduce a series of multiplicities associated to the extens...

Extensions of Several Integral Inequalities

In this article, an open problem posed in [12] is studied once again, and, following closely theorems and methods from [5], some extensions of several integral inequalities are obtained.

Separable integral extensions and plus closure

We show that an excellent local domain of characteristic p has a separable big Cohen–Macaulay algebra. In the course of our work we prove that an element which is in the Frobenius closure of an ideal can be forced into the expansion of the ideal to a module-finite separable extension ring.

INTEGRAL EXTENSIONS AND THE a-INVARIANT

In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if A ⊂ B is a finite homogeneous inclusion of standard graded domains over an algebraically closed field with A normal and B of minimal multiplicity then A has minimal multiplicity. In some sense these results are algebraic generalizations of Hurwitz type theorems.

On New Extensions of Hilbert's Integral Inequality