List questions from extension-field | MathQa

Example of an algebraic extension which is not a radical extension

Published on 12 Jan 2025 - 9:01

Is there concrete example of finite extension which is not normal?

Published on 12 Jan 2025 - 9:01

Are there non-abelian totally real extensions?

Published on 03 Jan 2025 - 12:41

Does a field extension equal $F(\alpha) = a_0+a_1\alpha+a_2\alpha^2+a_3\alpha^3+\cdots$

Published on 12 Jan 2025 - 23:36

The trace of $F|K$ is non degenerate if and only if the trace of $E\otimes_{K}F|E$ is nondegenerate

Published on 12 Jan 2025 - 9:01

Applications for $\mathbb Q(\sqrt 2)$

Published on 12 Jan 2025 - 9:01

If $\{a_{1},\ldots,a_{n}\}$ is a $K$-basis of $F$, then $\{1\otimes a_{1},\ldots,1\otimes a_{n}\}$ is an $E$-basis of $E\otimes_{K} F$.

Published on 02 Jan 2025 - 12:50

Is $\mathbb{Q}(\sqrt{2+\sqrt{-5}})$ normal over $\mathbb{Q}$

Published on 12 Jan 2025 - 9:01

Comparing degrees of field extensions: compositum over field versus field over intersection.

Published on 12 Jan 2025 - 9:01

Let $E$ be an algebraic extension of $F$. If every polynomial in $F[x]$ splits in $E$, show that $E$ is algebraically closed.

Published on 12 Jan 2025 - 9:01