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Results tagged with ac.commutative-algebra
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user 1729
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
15
votes
Why are finitely generated modules over principal artin local rings direct sums of cyclic mo...
First, all ideals are of the form $(\pi^i)$. Say $(\pi^n)$ is the annihilator of $M$. We can replace $A$ by $A/(\pi^n)$ wlog. Then $M$ has $A$ as submodule, since there's an element that isn't killed …
- 1,388
6
votes
Accepted
Finitely-generated algebra over Z
Take $A$ local (you already reduced to it), with $m$ the max. ideal. I claim that $A/m$ is a finite field. Suppose first that it has char. 0. Then we get injections $\mathbb Z \to \mathbb Q \to A/m$. …
- 1,388