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Results tagged with ac.commutative-algebra
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user 10147
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
11
votes
Accepted
What conditions are needed for $-\otimes_A B$ to be faithful?
The functor you mention is faithful if and only if the functor $-\bigotimes_A B :A-mod\to A-mod$ is faithful, ie iff $B$ is a faithful $A$-module.
For a concrete counterexample take $f:\mathbb{Z}\to …
- 441
12
votes
1
answer
2k
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Is every ring the direct limit of Noetherian rings?
Are there any examples of commutative rings that do not occur as direct limits of Noetherian rings?
- 441