query: When $\mathbb{A}^{n}_{k}$ is read as affine-n space over a field k...
positive_passages.docid: 27230
positive_passages.text: What *is* affine space?
negative_passages.docid: 126930
negative_passages.text: Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 115782
negative_passages.text: Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
negative_passages.docid: 79450
negative_passages.text: For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
negative_passages.docid: 34670
negative_passages.text: What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?
negative_passages.docid: 118513
negative_passages.text: Ideal of product of affine varieties
negative_passages.docid: 723
negative_passages.text: Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 38549
negative_passages.text: $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
negative_passages.docid: 155266
negative_passages.text: Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
negative_passages.docid: 17748
negative_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
negative_passages.docid: 89533
negative_passages.text: $\mathcal{K}(L^2(\mathbb{R}^m \times \mathbb{R}^n)) = \mathcal{K}(L^2(\mathbb{R}^m)) \otimes \mathcal{K}(L^2(\mathbb{R}^n))$?
negative_passages.docid: 111338
negative_passages.text: Affine variety over a field which is not algebraically closed can be written as the zero set of a single polynomial
negative_passages.docid: 63465
negative_passages.text: Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
negative_passages.docid: 104374
negative_passages.text: Diagonalizability of an involution over a Field
negative_passages.docid: 61761
negative_passages.text: Equivalent definition $\text{Cone}(K)$