query: If $\phi$ : $F_2[X]/(X^3+X+1)$ $\rightarrow$ $F_2[X]/(X^3+X^2+1)$ is an isomorphism, then prove that $\phi(a)=b+1$, with $a$, $b$ the classes of $X$
positive_passages.docid: 115129
positive_passages.text: Constructing an explicit isomorphism between finite extensions of finite fields
negative_passages.docid: 73652
negative_passages.text: Exhibiting an isomorphism between two finite fields
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: 46147
negative_passages.text: Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
negative_passages.docid: 127491
negative_passages.text: Isometric isomorphism between $R^2$ and $R$
negative_passages.docid: 26233
negative_passages.text: $[K(\zeta_n):K]=\phi(n)$?
negative_passages.docid: 78118
negative_passages.text: Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
negative_passages.docid: 141911
negative_passages.text: Prove that these two fields are isomorphic.
negative_passages.docid: 100439
negative_passages.text: Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$
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: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 147667
negative_passages.text: Polynomial ring isomorphisms
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 18540
negative_passages.text: Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 117681
negative_passages.text: For which Natural $n\ge2: \phi(n)=n/2$
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$