query: Prove an isomorphism between this two algebraic objects
positive_passages.docid: 141911
positive_passages.text: Prove that these two fields are isomorphic.
negative_passages.docid: 121465
negative_passages.text: $R[x]$ has a subring isomorphic to $R$.
negative_passages.docid: 52088
negative_passages.text: Isomorphism of an endomorphism ring, how can $R\cong R^2$?
negative_passages.docid: 108156
negative_passages.text: Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
negative_passages.docid: 3778
negative_passages.text: If the matrix rings over two Rings of the same size are isomorphic, then the scalar rings are isomorphic
negative_passages.docid: 83001
negative_passages.text: Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
negative_passages.docid: 149973
negative_passages.text: Showing the following coordinate rings are not isomorphic
negative_passages.docid: 115129
negative_passages.text: Constructing an explicit isomorphism between finite extensions of finite fields
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: 42362
negative_passages.text: Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals
negative_passages.docid: 36980
negative_passages.text: Prove the third isomorphism theorem
negative_passages.docid: 92599
negative_passages.text: Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
negative_passages.docid: 102371
negative_passages.text: Proving that two vector spaces of equal dimension are isomorphic
negative_passages.docid: 148881
negative_passages.text: Aut(GxH) isomorphic to Aut(G)xAut(H)
negative_passages.docid: 29359
negative_passages.text: Localisation isomorphic to a quotient of polynomial ring
negative_passages.docid: 130363
negative_passages.text: Prove composition of two surjections is surjection
negative_passages.docid: 126790
negative_passages.text: Basic Isomorphism Question