query: Consecuence of the existence of isomorphism $\mathbb{R}^3\rightarrow \mathfrak{o}(3)$
positive_passages.docid: 26110
positive_passages.text: Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 119648
negative_passages.text: For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 56234
negative_passages.text: Isomorphism $f$ preserves the order of an element?
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$
negative_passages.docid: 145462
negative_passages.text: On the canonical isomorphism between $V$ and $V^{**}$
negative_passages.docid: 62711
negative_passages.text: Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
negative_passages.docid: 116168
negative_passages.text: Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
negative_passages.docid: 158975
negative_passages.text: Isomorphism of centers of isomorphic groups
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
negative_passages.docid: 112131
negative_passages.text: Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
negative_passages.docid: 86748
negative_passages.text: Isomorphism of hom sets implies objects are isomorphic
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 97608
negative_passages.text: Showing a Ring of endomorphisms is isomorphic to a Ring