List questions from field-theory

Published on 29 Mar 2026 - 15:02

1.2k

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Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

Published on 26 Mar 2026 - 1:23

234

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Let $\alpha: F \rightarrow F$ be a one to one field homomorphism, prove $\alpha$ fixes the prime subfield of $F$ elementwise

Published on 01 Apr 2026 - 19:09

55

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If $L/K$ is algebraic, is $L$ a subfield of some algebraic closure $\bar K$ of $K$?

Published on 27 Mar 2026 - 13:20

209

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Show that $L_N$ is the Galois closure of $K$

Published on 29 Mar 2026 - 18:51

153

Views

Determining the Galois Group of Splitting Field of Cubic polynomials

Published on 29 Mar 2026 - 20:33

66

Views

Field extensions confusion

Published on 29 Mar 2026 - 16:33

242

Views

Extending Isomorphisms

Published on 26 Mar 2026 - 23:33

80

Views

Use induction to prove that $(a+b)^{p^n}=a^{p^n}+b^{p^n}$

Published on 01 Apr 2026 - 19:13

71

Views

Expressiong $\frac{t+2}{t^3+3}$ in the form $a_o+a_1t+...+a_4t^4$, where $t$ is a root of $x^5+2x+2$

Published on 01 Apr 2026 - 19:15

1.4k

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Is every primitive element of a finite field of characteristic $2$, a generator of the multiplicative group?

Published on 27 Mar 2026 - 10:13

509

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Generators/primitive roots/primitive elements of Prime fields

Published on 27 Mar 2026 - 15:05

260

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Generalizations of the field concept to triplets of elements

Published on 02 Apr 2026 - 13:25

85

Views

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

Published on 29 Mar 2026 - 16:35

99

Views

The degree of a field extension

Published on 29 Mar 2026 - 20:31

List Question

On the number of embeddings in algebraic closure.

Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

Let $\alpha: F \rightarrow F$ be a one to one field homomorphism, prove $\alpha$ fixes the prime subfield of $F$ elementwise

If $L/K$ is algebraic, is $L$ a subfield of some algebraic closure $\bar K$ of $K$?

Show that $L_N$ is the Galois closure of $K$

Determining the Galois Group of Splitting Field of Cubic polynomials

Field extensions confusion

Extending Isomorphisms

Use induction to prove that $(a+b)^{p^n}=a^{p^n}+b^{p^n}$

Expressiong $\frac{t+2}{t^3+3}$ in the form $a_o+a_1t+...+a_4t^4$, where $t$ is a root of $x^5+2x+2$

Is every primitive element of a finite field of characteristic $2$, a generator of the multiplicative group?

Generators/primitive roots/primitive elements of Prime fields

Generalizations of the field concept to triplets of elements

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

The degree of a field extension

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