query: When are the 2 fields isomorphic?
positive_passages.docid: 18048
positive_passages.text: Easy criteria to determine isomorphism of fields?
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 72478
negative_passages.text: What is the isomorphism between the fields $(Z_2[x]^{<3},+_{x^3+x^2+1},\times_{x^3+x^2+1})$ and $(Z_2[x]^{<3},+_{x^3+x+1},\times_{x^3+x+1})$?
negative_passages.docid: 7010
negative_passages.text: Example of two non-isomorphic fields which embed inside each other
negative_passages.docid: 120811
negative_passages.text: What does "isomorphic" mean in linear algebra?
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: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 94579
negative_passages.text: $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
negative_passages.docid: 121449
negative_passages.text: An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
negative_passages.docid: 146334
negative_passages.text: Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 25793
negative_passages.text: Extension fields isomorphic to fields of matrices
negative_passages.docid: 86174
negative_passages.text: Finding an isomorphism between these two finite fields
negative_passages.docid: 45179
negative_passages.text: When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?