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Answer by Z. M for Faithful flatness and non-commutative algebras
There is a simple criterion. I learned from Jacob Lurie's paper Tannaka Duality for Geometric Stacks, Lemma 5.5. His argument works, but since his statement does not cover the current situation, let me...
View ArticleFaithful flatness and non-commutative algebras
When dealing with commutative algebras, a usefull criterion for faithfull flatness is the following:Let $f:A\rightarrow B$ be a morphism of commutative algebras. Then $f$ is faithfully flat if and only...
View ArticleAnswer by Simon Wadsley for Faithful flatness and non-commutative algebras
If $A$ happens to be (left) Noetherian then to show $f$ makes $B$ a faithfully flat right $A$-module it is enough to check that $B\otimes_A S\neq 0$ for every simple (left) $A$-module $S$ since, in...
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