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Results tagged with ac.commutative-algebra
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user 12208
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
11
votes
Is being finitely generated a local property?
Suppose we have an element $x\in B$. Then it's image in $B_{f_i}$ is equal to some $F^i( \frac{b^i_1}{f_i^{k^i_1}} ,\ldots ,\frac{b^i_{j_i}}{f_i^{k^i_{j_i}}})$, where $\frac{b^i_j}{f_i^{k^i_j}}$ are t …
- 420
0
votes
CM for primary ideal
I think it's true. R/I being CM means depth(R/I)=dim(R/I). But as R/I is a factor of R/J by nilradical it follows that dim(R/J)=dim(R/I). As R/I is a factorring of R/J we also have depth(R/I)$\leq$dep …
- 420