query: Dimension of an extension of a field
positive_passages.docid: 28313
positive_passages.text: Intermediate ring between a field and an algebraic extension.
negative_passages.docid: 75829
negative_passages.text: Dimension of open subsets of $R^n$
negative_passages.docid: 153589
negative_passages.text: Integral basis of an extension of number fields
negative_passages.docid: 127796
negative_passages.text: Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
negative_passages.docid: 34990
negative_passages.text: Ring homomorphism defined on a field
negative_passages.docid: 68065
negative_passages.text: Quadratic extensions in characteristic $2$
negative_passages.docid: 145140
negative_passages.text: Subfield of $\mathbb{Q}(\sqrt[n]{a})$
negative_passages.docid: 74764
negative_passages.text: Dimension for a closed subspace of $C[0,1]$.
negative_passages.docid: 79450
negative_passages.text: For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
negative_passages.docid: 79725
negative_passages.text: Fields of arbitrary cardinality
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: 80295
negative_passages.text: Field extensions and algebraic/transcendental elements
negative_passages.docid: 25793
negative_passages.text: Extension fields isomorphic to fields of matrices
negative_passages.docid: 51770
negative_passages.text: Number of elements in a finite field extension for finite fields
negative_passages.docid: 27577
negative_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 41815
negative_passages.text: Galois extension of intersection of fields
negative_passages.docid: 142707
negative_passages.text: Intermediate fields of a finite field extension that is not separable