query: Any epi with codomain $P$ is split implies $P$ is projective
positive_passages.docid: 16768
positive_passages.text: Different definitions of projective objects
negative_passages.docid: 2907
negative_passages.text: How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 148633
negative_passages.text: Description of varieties in $\mathbb{P}^2\times \mathbb{P}^1$
negative_passages.docid: 96618
negative_passages.text: Any finite set of points in in the projective plane can be defined by two polynomials
negative_passages.docid: 31216
negative_passages.text: Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?
negative_passages.docid: 115347
negative_passages.text: Showing that the fiber of a morphism of schemes over a point is homeomorphic to the preimage
negative_passages.docid: 92574
negative_passages.text: Can an algebraic variety be embedded in projective space?
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 84437
negative_passages.text: Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
negative_passages.docid: 27086
negative_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 155991
negative_passages.text: Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
negative_passages.docid: 149999
negative_passages.text: fixed point of a continuous map on a projective space
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 113391
negative_passages.text: Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too.
negative_passages.docid: 106081
negative_passages.text: The Projection to a Projective Line is Holomorphic
negative_passages.docid: 51465
negative_passages.text: New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$