query: Proof on simple extension
positive_passages.docid: 126127
positive_passages.text: A field extension of prime degree
negative_passages.docid: 78941
negative_passages.text: proof that an alternative definition of limit is equivalent to the usual one
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: 52429
negative_passages.text: Explicit countable elementary extension of $\mathbb{N}$
negative_passages.docid: 39755
negative_passages.text: In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
negative_passages.docid: 107281
negative_passages.text: Proof of Existence of Algebraic Closure: Too simple to be true?
negative_passages.docid: 134588
negative_passages.text: Seeking a direct proof about nested inclusions
negative_passages.docid: 21391
negative_passages.text: Proving Functions are Surjective
negative_passages.docid: 28272
negative_passages.text: Does such localization of integral extension preserve inclusion?
negative_passages.docid: 147908
negative_passages.text: Why use the biconditional in the Axiom of Extensionality
negative_passages.docid: 144713
negative_passages.text: Simple Calculus Proof
negative_passages.docid: 154363
negative_passages.text: Prove that $\text{aff}(X) = \text{aff}(\text{closure}(X))$
negative_passages.docid: 106737
negative_passages.text: A problem on field extension
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 25874
negative_passages.text: Showing that a certain map is not flat by explicit counterexample
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 883
negative_passages.text: $K(u,v)$ is a simple extension of fields if $u$ is separable