query: Is the class of algebraic extensions distinguished?
positive_passages.docid: 147569
positive_passages.text: Algebraic Property inherited by a "lift"?
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 129153
negative_passages.text: Is it Galois extension?
negative_passages.docid: 61429
negative_passages.text: Is the algebraic closure of a $p$-adic field complete
negative_passages.docid: 143219
negative_passages.text: If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
negative_passages.docid: 883
negative_passages.text: $K(u,v)$ is a simple extension of fields if $u$ is separable
negative_passages.docid: 130186
negative_passages.text: Zero module of differentials implies finite extension?
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 68790
negative_passages.text: Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?
negative_passages.docid: 83595
negative_passages.text: Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
negative_passages.docid: 93111
negative_passages.text: Finiteness of the Algebraic Closure
negative_passages.docid: 128550
negative_passages.text: Algebraic field extension and intermediate integral domain
negative_passages.docid: 66355
negative_passages.text: A sufficient condition for irreducibility of a polynomial in an extension field.
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 111444
negative_passages.text: Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
negative_passages.docid: 81550
negative_passages.text: Linking two theorems: on algebraic closure and on minimal splitting field
negative_passages.docid: 80538
negative_passages.text: Fields extensions over isomorphic fields of different degrees