List questions from field-theory

Published on 14 Apr 2026 - 12:11

41

Views

If $W$ and $V$ are vector spaces what is $\Pi(W \oplus V)$?

Published on 13 Apr 2026 - 9:34

858

Views

Given a ring, when can I find a field that extends it making it a subring?

Published on 12 Apr 2026 - 22:45

62

Views

Explicit polynomial over $\mathbb{F}_p$ mapping roots of irreducibles

Published on 15 Apr 2026 - 20:05

1.1k

Views

Proof of Wilson's theorem via finite fields?

Published on 13 Apr 2026 - 15:54

786

Views

Abstract Algebra - Minimal Polynomials

Published on 15 Apr 2026 - 18:49

2.3k

Views

Proof of extension field containing a root of irreducible polynomial

Published on 12 Apr 2026 - 1:43

342

Views

Showing that a certain field extension is Galois

Published on 13 Apr 2026 - 11:17

177

Views

Semi-simple quadratic extension over $\mathbb{Q}$

Published on 20 Apr 2026 - 9:27

456

Views

Field Extension Notation Indicative of Quotient Object

Published on 05 May 2026 - 3:26

775

Views

Field extension of finite fields are always separable?

Published on 12 Apr 2026 - 4:45

766

Views

What are the integers of $\textbf Q(\sqrt 2 + i)$?

Published on 14 Apr 2026 - 1:33

7.2k

Views

A method to count the number of monic irreducible polynomials of degree 2 or 3 or 4 in $\mathbb F_{p}[x]$

Published on 17 Apr 2026 - 15:45

212

Views

Splitting field of polynomial generated by just one of its roots

Published on 17 Apr 2026 - 11:13

215

Views

Algebraically dependent vs. one element can be expressed as a polynomial of the others

Published on 10 May 2026 - 23:27

List Question

Irreducible polynomial in field extension

If $W$ and $V$ are vector spaces what is $\Pi(W \oplus V)$?

Given a ring, when can I find a field that extends it making it a subring?

Explicit polynomial over $\mathbb{F}_p$ mapping roots of irreducibles

Proof of Wilson's theorem via finite fields?

Abstract Algebra - Minimal Polynomials

Proof of extension field containing a root of irreducible polynomial

Showing that a certain field extension is Galois

Semi-simple quadratic extension over $\mathbb{Q}$

Field Extension Notation Indicative of Quotient Object

Field extension of finite fields are always separable?

What are the integers of $\textbf Q(\sqrt 2 + i)$?

A method to count the number of monic irreducible polynomials of degree 2 or 3 or 4 in $\mathbb F_{p}[x]$

Splitting field of polynomial generated by just one of its roots

Algebraically dependent vs. one element can be expressed as a polynomial of the others

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