query: If R[X] isomorphic to S[X] then R isomorphic to S?
positive_passages.docid: 18330
positive_passages.text: Does $R[x] \cong S[x]$ imply $R \cong S$?
negative_passages.docid: 69160
negative_passages.text: Show that the functor that takes $R$ to the set of invertible elements of $R[X]/(X^2-a)$ is representable.
negative_passages.docid: 157840
negative_passages.text: Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
negative_passages.docid: 48537
negative_passages.text: If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
negative_passages.docid: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 157040
negative_passages.text: For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$?
negative_passages.docid: 120968
negative_passages.text: Isomorphism of stabilizer over $S_n$ to $S_{n-1}$
negative_passages.docid: 55778
negative_passages.text: Group theoretic meaning of natural isomorphisms between certain functors
negative_passages.docid: 40793
negative_passages.text: What is the difference betwen equivalence and isomorphism of functors in categories.
negative_passages.docid: 99382
negative_passages.text: What is needed to make Euclidean spaces isomorphic as groups?
negative_passages.docid: 15312
negative_passages.text: Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems
negative_passages.docid: 23579
negative_passages.text: If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$