query: Let $k$ be an algebraically closed field. How do we show $Y=\{(t, t^2, t^3) \mid t \in k\}$ is an algebraic set?
positive_passages.docid: 145865
positive_passages.text: Showing a set is an affine variety
negative_passages.docid: 90599
negative_passages.text: Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
negative_passages.docid: 63104
negative_passages.text: Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$
negative_passages.docid: 143219
negative_passages.text: If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
negative_passages.docid: 157488
negative_passages.text: Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
negative_passages.docid: 82824
negative_passages.text: Affine algebraic subset of $\mathbb{A}_k^4$
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: 76640
negative_passages.text: Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
negative_passages.docid: 16163
negative_passages.text: Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
negative_passages.docid: 46565
negative_passages.text: Show that $\mathbb{Q}(\sqrt{2})$ is a field.
negative_passages.docid: 77862
negative_passages.text: Question about fields and quotients of polynomial rings
negative_passages.docid: 149820
negative_passages.text: How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?
negative_passages.docid: 126427
negative_passages.text: Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
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: 128550
negative_passages.text: Algebraic field extension and intermediate integral domain
negative_passages.docid: 34740
negative_passages.text: Do finite algebraically closed fields exist?