query: Union of subextensions of an Extension field is still a field.
positive_passages.docid: 156038
positive_passages.text: Why does Lang describe a field as a union and compositum of its subfields in this manner?
negative_passages.docid: 120943
negative_passages.text: Galois field extension and number of intermediate fields
negative_passages.docid: 883
negative_passages.text: $K(u,v)$ is a simple extension of fields if $u$ is separable
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: 111347
negative_passages.text: Finding an example of field extensions satisfying certain properties
negative_passages.docid: 111444
negative_passages.text: Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
negative_passages.docid: 101869
negative_passages.text: Field Extension Notation
negative_passages.docid: 71102
negative_passages.text: Subfields of $\mathbb{C}$ which are connected with induced topology
negative_passages.docid: 115129
negative_passages.text: Constructing an explicit isomorphism between finite extensions of finite fields
negative_passages.docid: 82328
negative_passages.text: Constructing a Galois extension field with Galois group $S_n$
negative_passages.docid: 58424
negative_passages.text: If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
negative_passages.docid: 45642
negative_passages.text: Prove that the Extension Theorem is Complete.
negative_passages.docid: 101098
negative_passages.text: Field extensions with(out) a common extension
negative_passages.docid: 144245
negative_passages.text: Shorter proof of $R/I$ is a field if and only if $I$ is maximal
negative_passages.docid: 68753
negative_passages.text: Elements in finite field extensions
negative_passages.docid: 79450
negative_passages.text: For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$