query: Give an example of fields $k\subseteq K\subseteq L $, and $l\subseteq L$, for which $l/k$ and $L/K$ are algebraic, $k$ is algebraically closed
positive_passages.docid: 111347
positive_passages.text: Finding an example of field extensions satisfying certain properties
negative_passages.docid: 6855
negative_passages.text: Subfields of finite fields
negative_passages.docid: 28313
negative_passages.text: Intermediate ring between a field and an algebraic extension.
negative_passages.docid: 61084
negative_passages.text: Examples of non-isomorphic fields with isomorphic group of units and additive group structure
negative_passages.docid: 98577
negative_passages.text: Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
negative_passages.docid: 63390
negative_passages.text: Infinite algebraic extensions of $\mathbb{Q}$
negative_passages.docid: 48162
negative_passages.text: Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
negative_passages.docid: 31961
negative_passages.text: Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?
negative_passages.docid: 64502
negative_passages.text: On the meaning of being algebraically closed
negative_passages.docid: 47041
negative_passages.text: What are the conditions for integers $D_1$ and $D_2$ so that $\mathbb{Q}[\sqrt {D_1}] \simeq \mathbb{Q}[\sqrt {D_2}]$ as fields.
negative_passages.docid: 7010
negative_passages.text: Example of two non-isomorphic fields which embed inside each other
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: 157420
negative_passages.text: Question about Subrings and integraly closed
negative_passages.docid: 113216
negative_passages.text: No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$
negative_passages.docid: 111338
negative_passages.text: Affine variety over a field which is not algebraically closed can be written as the zero set of a single polynomial
negative_passages.docid: 158525
negative_passages.text: Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?
negative_passages.docid: 81550
negative_passages.text: Linking two theorems: on algebraic closure and on minimal splitting field