query: Field of fractions of integral extension is an algebraic extension
positive_passages.docid: 151236
positive_passages.text: Question related to integrality of field of fractions
negative_passages.docid: 109647
negative_passages.text: Ext$_R^n(Q,A)=0=$Tor$_n^R(Q,A)$ where $Q$ is the field of fractions of a domain $R$
negative_passages.docid: 69935
negative_passages.text: Field extensions of finite degree and primitive elements
negative_passages.docid: 141410
negative_passages.text: Injective integral domains are fields
negative_passages.docid: 68753
negative_passages.text: Elements in finite field extensions
negative_passages.docid: 25793
negative_passages.text: Extension fields isomorphic to fields of matrices
negative_passages.docid: 19525
negative_passages.text: Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
negative_passages.docid: 76496
negative_passages.text: Showing that every field is an integral domain.
negative_passages.docid: 50668
negative_passages.text: Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
negative_passages.docid: 134896
negative_passages.text: Enlightening proof that the algebraic numbers form a field
negative_passages.docid: 63390
negative_passages.text: Infinite algebraic extensions of $\mathbb{Q}$
negative_passages.docid: 41505
negative_passages.text: Transcendental Extensions. $F(\alpha)$ isomorphic to $F(x)$
negative_passages.docid: 48093
negative_passages.text: Irreducible polynomial in field extension
negative_passages.docid: 41815
negative_passages.text: Galois extension of intersection of fields
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 883
negative_passages.text: $K(u,v)$ is a simple extension of fields if $u$ is separable
negative_passages.docid: 14270
negative_passages.text: Polynomial divisibility is unchanged by coeff. field extension