Tag Archives: nilradical

Commutative Algebra 38

Posted on April 26, 2020 by limsup

Artinian Rings The main result we wish to prove is the following. Theorem. A ring A is artinian if and only if it is noetherian and , where denotes the Krull dimension. Note Recall that means all prime ideals of A … Continue reading →

Posted in Advanced Algebra | Tagged , , , | Leave a comment

Commutative Algebra 14

Posted on April 1, 2020 by limsup

Basic Open Sets For , let , an open subset of Spec A. Note that . Proposition 1. The collection of over all forms a basis for the topology of . Proof Let be an open subset of Spec A. Suppose … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , , , , | Leave a comment