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About Fulton's Intersection theory Appendix Lemma A 4.1

No. Whereas $A/I\otimes_A B=B/IB$ by right-exactness $I\otimes_A B\to IB$ is not an isomorphism in general. The exact sequence $$0\to I_{i-1}\to I_i\to I_i/I_{i-1} \to 0$$ only gives rise to the right …
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