Tag Archives: normal domains

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 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 →

Posted in Advanced Algebra | Tagged , , , , , , | 7 Comments

Commutative Algebra 39

Posted on April 27, 2020 by limsup

Integrality Throughout this article, A is a subring of B; we will also call B a ring extension of A. Definition. An element is said to be integral over A if we can find (where ) such that in B. For example, is integral over since … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , , | 4 Comments