query: Show that $K$ is a field
positive_passages.docid: 155165
positive_passages.text: Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
negative_passages.docid: 135046
negative_passages.text: Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
negative_passages.docid: 145726
negative_passages.text: For a subfield $K$ of $\Bbb C$ with $K\nsubseteq \Bbb R$, show $K$ is dense in $\Bbb C$.
negative_passages.docid: 137278
negative_passages.text: Quotient field of gaussian integers
negative_passages.docid: 134439
negative_passages.text: Proving function is $C^k$
negative_passages.docid: 11698
negative_passages.text: $M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
negative_passages.docid: 144245
negative_passages.text: Shorter proof of $R/I$ is a field if and only if $I$ is maximal
negative_passages.docid: 10111
negative_passages.text: Prove or disprove that Q[√2] is a field
negative_passages.docid: 85096
negative_passages.text: Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
negative_passages.docid: 4401
negative_passages.text: Constructive proof that algebraic numbers form a field
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: 13606
negative_passages.text: Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
negative_passages.docid: 111129
negative_passages.text: Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 147069
negative_passages.text: Intersection of field extensions
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 51706
negative_passages.text: If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$