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Answer 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...
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 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...
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