Tag Archives: associated primes

Commutative Algebra 60

Posted on May 18, 2020 by limsup

Primary Decomposition of Ideals Definition. Let be a proper ideal. A primary 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 →

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

Commutative Algebra 59

Posted on May 17, 2020 by limsup

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 →

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

Commutative Algebra 58

Posted on May 16, 2020 by limsup

We have already seen two forms of unique factorization. In a UFD, every non-zero element is a unique product of irreducible (also prime) elements. In a Dedekind domain, every non-zero ideal is a unique product of maximal ideals. Here, we … Continue reading →

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