query: $F$ is isomorphic to $\Bbb Z_p$ for some prime number $p$.
positive_passages.docid: 149849
positive_passages.text: Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
negative_passages.docid: 143451
negative_passages.text: Homomorphism from $(\Bbb Q,+)$ to a finite group
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: 37929
negative_passages.text: Classification of prime ideals of $\mathbb{Z}[X]$
negative_passages.docid: 93017
negative_passages.text: Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
negative_passages.docid: 37351
negative_passages.text: Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
negative_passages.docid: 136422
negative_passages.text: Two finite fields with the same number of elements are isomorphic
negative_passages.docid: 62615
negative_passages.text: If F is a finite field, then $F^F=P_F$.
negative_passages.docid: 52530
negative_passages.text: There exists a prime congruent to $m$ mod $p$
negative_passages.docid: 115299
negative_passages.text: Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 39843
negative_passages.text: Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$
negative_passages.docid: 74370
negative_passages.text: $P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 110662
negative_passages.text: Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
negative_passages.docid: 56234
negative_passages.text: Isomorphism $f$ preserves the order of an element?