query: When $M^{**} \cong M$
positive_passages.docid: 145700
positive_passages.text: Module isomorphic to second dual
negative_passages.docid: 27056
negative_passages.text: $ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $
negative_passages.docid: 133500
negative_passages.text: For an outer measure $m^*$, does $m^*(E\cup A)+m^*(E\cap A) = m^*(E)+m^*(A)$ always hold?
negative_passages.docid: 17191
negative_passages.text: How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$
negative_passages.docid: 18330
negative_passages.text: Does $R[x] \cong S[x]$ imply $R \cong S$?
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 52642
negative_passages.text: Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
negative_passages.docid: 62879
negative_passages.text: Question about the proof of $GCH$ holds in $\mathbf L$
negative_passages.docid: 73235
negative_passages.text: Rings $R/I \cong h(R)/h(I)\,$ for injective ring hom $h$
negative_passages.docid: 4648
negative_passages.text: Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
negative_passages.docid: 135422
negative_passages.text: $\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 115606
negative_passages.text: Proofs involving $ (A\setminus B) \cup (A \cap B)$
negative_passages.docid: 140471
negative_passages.text: Is $ G \cong G/N \times N$?
negative_passages.docid: 30178
negative_passages.text: Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
negative_passages.docid: 52088
negative_passages.text: Isomorphism of an endomorphism ring, how can $R\cong R^2$?
negative_passages.docid: 87946
negative_passages.text: Proving that the unities of a ring form a group under multiplication