[Merged by Bors] - feat: the equational criterion for vanishing #12647
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Let $M$ and $N$ be modules over a commutative ring $R$. Following Lemma 8.16 of Altman and Kleiman's *A term of commutative algebra*, we prove some results about under what circumstances a sum of pure tensors $\sum_i m_i \otimes n_i \in M \otimes_R N$ vanishes. The *equational criterion for flatness* is not included in this pull request, but it is an easy consequence of these results.
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Let $M$ and $N$ be modules over a commutative ring $R$. Following Lemma 8.16 of Altman and Kleiman's *A term of commutative algebra*, we prove some results about under what circumstances a sum of pure tensors $\sum_i m_i \otimes n_i \in M \otimes_R N$ vanishes. The *equational criterion for flatness* is not included in this pull request, but it is an easy consequence of these results.
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Let $M$ and $N$ be modules over a commutative ring $R$. Following Lemma 8.16 of Altman and Kleiman's *A term of commutative algebra*, we prove some results about under what circumstances a sum of pure tensors $\sum_i m_i \otimes n_i \in M \otimes_R N$ vanishes. The *equational criterion for flatness* is not included in this pull request, but it is an easy consequence of these results.
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Let$M$ and $N$ be modules over a commutative ring $R$ . Following Lemma 8.16 of Altman and Kleiman's A term of commutative algebra, we prove some results about under what circumstances a sum of pure tensors $\sum_i m_i \otimes n_i \in M \otimes_R N$ vanishes. The equational criterion for flatness is not included in this pull request, but it is an easy consequence of these results.