List questions from field-theory

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Let K be field and L be a subfield prove that

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Solving system of equation over distinct finite fields

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Find the ring of algebraic integers.

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Can an orderable field always be ordered in a way that extends a given subfield's ordering?

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different factors of irreducible polynomials over a Galois extension does not share roots

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Subgroups of $\mathbb F_{p^n}$

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Algebraic extension of rational functions

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Why does this criterion imply that $A$ is a subfield of $E$?

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Problem with modulo in field

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Show that it is a subfield

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Show that $F = \{a + b\sqrt{5} | a, b ∈ \mathbb Q\}$ is a field

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What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$

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Does $\sum_{i=1}^nx_i=0$ and $\sum_{i=1}^nc_ix_i=0$ implies $c_i=c_j$ in a field?

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Diagrams characterizing ring characteristic, and in particular field characteristic 1?

Published on 25 Mar 2026 - 11:54

List Question

Reference Request for a book on Field Theory

Let K be field and L be a subfield prove that

Solving system of equation over distinct finite fields

Find the ring of algebraic integers.

Can an orderable field always be ordered in a way that extends a given subfield's ordering?

different factors of irreducible polynomials over a Galois extension does not share roots

Subgroups of $\mathbb F_{p^n}$

Algebraic extension of rational functions

Why does this criterion imply that $A$ is a subfield of $E$?

Problem with modulo in field

Show that it is a subfield

Show that $F = \{a + b\sqrt{5} | a, b ∈ \mathbb Q\}$ is a field

What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$

Does $\sum_{i=1}^nx_i=0$ and $\sum_{i=1}^nc_ix_i=0$ implies $c_i=c_j$ in a field?

Diagrams characterizing ring characteristic, and in particular field characteristic 1?

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