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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.
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
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