List questions from field-theory | MathQa

Does there exist a maximal Archimedean ordered field?

Published on 29 Dec 2024 - 2:55

If $f,g$ are non-zero polynomials and $f$ divides $g$, then $\partial f \leq \partial g$.

Published on 02 Jan 2025 - 12:35

Show that the quotient ring $R/\mathcal{I}$ is a field.

Published on 12 Jan 2025 - 9:03

Constructing finite fields of order $8$ and $27$ or any non-prime

Published on 25 Dec 2024 - 18:22

Prove there is a polynomial $P_0$ with the property that $\mathcal{I}$ consists precisely of the multiples of $P_0$.

Published on 28 Dec 2024 - 22:29

Example of an algebraic extension which is not a radical extension

Published on 12 Jan 2025 - 9:01

If the degree of $\alpha$ is prime, then it equals the degree of $\alpha^q$ for every other prime $q$?

Published on 05 Jan 2025 - 13:48

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

Published on 12 Jan 2025 - 9:01

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 - 9:01

Give $3$ examples of a field extensions which are neither normal nor separable.

Published on 24 Dec 2024 - 21:07