Tag Archives: primary decompositions

Commutative Algebra 63

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 60

Primary Decomposition of Ideals Definition. Let be a proper ideal. A┬áprimary decomposition of is its primary decomposition as an A-submodule of A: where each is -primary for some prime , i.e. . Here is a quick way to determine if … Continue reading

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Commutative Algebra 59

Prime Composition Series Throughout this article, A is a noetherian ring and all A-modules are finitely generated. Recall (proposition 1 here) that if M is a noetherian and artinian module, we can find a sequence of submodules whose consecutive factors … Continue reading

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