query: Every algebraic extension of a finite field $F$ is separable
positive_passages.docid: 157499
positive_passages.text: Every finite extension of a finite field is separable
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 19511
negative_passages.text: Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
negative_passages.docid: 74681
negative_passages.text: A finite extension with finitely many intermediate fields is simple
negative_passages.docid: 31831
negative_passages.text: Why every polynomial over the algebraic numbers $F$ splits over $F$?
negative_passages.docid: 136422
negative_passages.text: Two finite fields with the same number of elements are isomorphic
negative_passages.docid: 67157
negative_passages.text: Example of an non-normal inseparable field extension
negative_passages.docid: 146617
negative_passages.text: A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
negative_passages.docid: 7567
negative_passages.text: Degree of Field Extensions and $F(\alpha)$
negative_passages.docid: 27689
negative_passages.text: Separability over intersection of intermediate fields
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 74663
negative_passages.text: Is $\mathbb{R}$ an algebraic extension of some proper subfield?
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 79450
negative_passages.text: For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
negative_passages.docid: 128550
negative_passages.text: Algebraic field extension and intermediate integral domain
negative_passages.docid: 55764
negative_passages.text: Algebraic closure of $\mathbb F_p$
negative_passages.docid: 119305
negative_passages.text: Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?