Tag Archives: discrete valuation rings

Commutative Algebra 63

Posted on May 28, 2020 by limsup

Serre’s Criterion for Normality Throughout this article, fix an algebraically closed field k. In this section, A denotes a noetherian domain. We will describe Serre’s criterion, which is a necessary and sufficient condtion for A to be normal. In the … Continue reading →

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Commutative Algebra 46

Posted on May 4, 2020 by limsup

Properties of Dedekind Domains Throughout this article, A denotes a Dedekind domain. Proposition 1. Every fractional ideal of A can be written as where each is a maximal ideal. The expression is unique up to permutation of terms. Note In … Continue reading →

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Commutative Algebra 45

Posted on May 3, 2020 by limsup

Invertibility is Local In this article, we again let A be an integral domain and K its field of fractions. We continue our discussion of invertible fractional ideals of A. Proposition 1. A fractional ideal M of A is invertible if and … Continue reading →

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