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Results tagged with ac.commutative-algebra
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user 19576
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
0
votes
2
answers
331
views
finite global dimension vs integral Domain
For the quotient of polynomial rings over complex number field,
its global dimension is finite is equivalent to it is domain.
is this true?
- 77
1
vote
1
answer
446
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Does the global dimension gldim R equal the projective dimension of R as bimodule over its e...
I know that generally the answer is no, for example the weyl algebra。
But is this true for commutative algebra？ or we may restrict to affine commutative algebras。
Maybe ，it is a classical result. So …
- 77
5
votes
6
answers
4k
views
an easy example of valuation ring which is not noetherian？ [duplicate]
Is there an easy example of valuation ring which is not noetherian？
- 77
-1
votes
1
answer
752
views
Question on an exercise on homological algebra?
Suppose $R$ has finite global dimension $n$, $N$ is a finitely generated module, $F$ is a free module, and $\operatorname{Ext}^n(N, F) \neq 0$. Then $\operatorname{Ext}^n(N, R)$ is also non-trivial.
N …
- 77