query: Proving a map $M/\mathfrak{m}M\to M\otimes_S k$ is isomorphism.
positive_passages.docid: 157236
positive_passages.text: Tensor product of modules.
negative_passages.docid: 130367
negative_passages.text: Proof that $K\otimes_F L$ is not noetherian
negative_passages.docid: 121449
negative_passages.text: An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
negative_passages.docid: 129704
negative_passages.text: Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism?
negative_passages.docid: 52354
negative_passages.text: Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 147564
negative_passages.text: Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
negative_passages.docid: 59566
negative_passages.text: Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
negative_passages.docid: 154847
negative_passages.text: homomorphism from $S_3$ to $\mathbb Z/3\mathbb Z$
negative_passages.docid: 17191
negative_passages.text: How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$
negative_passages.docid: 26661
negative_passages.text: Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
negative_passages.docid: 58707
negative_passages.text: Prove Quotient Group Isomorphism
negative_passages.docid: 6101
negative_passages.text: Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
negative_passages.docid: 141258
negative_passages.text: Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
negative_passages.docid: 40490
negative_passages.text: Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
negative_passages.docid: 107163
negative_passages.text: Proof that $S_3$ isomorphic to $D_3$
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$