Computing Integral Closure Workshop

On Computing the Integral Closure1

We note how to apply the integral closure algorithm of de Jong to a reduced algebra finitely generated over the integers, and that the first step in Vasconcelos’ integral closure algorithm can by bypassed.

An algorithm for computingthe integral closure

Leonard and Pellikaan [2003] devised an algorithm for computing the integral closure of weighted rings that are finitely generated over finite fields. Previous algorithms proceed by building successively larger rings between the original ring and its integral closure [de Jong 1998; Seidenberg 1970; 1975; Stolzenberg 1968; Vasconcelos 1991; 2000]; the Leonard–Pellikaan algorithm instead starts w...

On the algebraicity of generalized power series

Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn-Mal’cev-Neumann generalized power series. We then give a corrected characterization, generalizing our earlier description in terms of finite automata in the case where...

AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS

In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.

Computing the Integral Closure of an Affine Semigroup