query: Every finite extension of the field with characteristics $0$ is simple extension.
positive_passages.docid: 151978
positive_passages.text: Splitting field of x^3-2 as a simple extension
negative_passages.docid: 51770
negative_passages.text: Number of elements in a finite field extension for finite fields
negative_passages.docid: 146446
negative_passages.text: Infinite Degree Algebraic Field Extensions
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 136422
negative_passages.text: Two finite fields with the same number of elements are isomorphic
negative_passages.docid: 151018
negative_passages.text: Proving that any finite integral domain is a field.
negative_passages.docid: 79450
negative_passages.text: For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
negative_passages.docid: 14343
negative_passages.text: Every nonzero element in a finite ring is either a unit or a zero divisor
negative_passages.docid: 106660
negative_passages.text: Every subgroup of the integers has finite index
negative_passages.docid: 34740
negative_passages.text: Do finite algebraically closed fields exist?
negative_passages.docid: 107370
negative_passages.text: An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
negative_passages.docid: 129597
negative_passages.text: Is a field perfect iff the primitive element theorem holds for all extensions, and what about function fields
negative_passages.docid: 41061
negative_passages.text: Simple property of a valuation on a field
negative_passages.docid: 110345
negative_passages.text: Examples of fields of characteristic 0?
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 132423
negative_passages.text: Non trivial valuation over a finite extension $F/\mathbb{Q}_p$ is equivalent to the one induced by $v_p$
negative_passages.docid: 14270
negative_passages.text: Polynomial divisibility is unchanged by coeff. field extension