Questions tagged [field-theory]
Use this tag for questions about fields and field theory in abstract algebra. A field is, roughly speaking, an algebraic structure in which addition, subtraction, multiplication, and division of elements are well-defined. This tag is NOT APPROPRIATE for questions about the fields you encounter in multivariable calculus or physics. Use (vector-fields) for questions on that theme instead.
2 questions from the last 7 days
2
votes
1
answer
137
views
Prove that $\mathbb{Q}(\alpha, \beta, \gamma, r_1) = \mathbb{Q}(r_1, r_2, r_3, r_4)$
Problem Statement: Let $f(x) = x^4 + ax^3 + bx^2 + cx + d$ be an irreducible polynomial over the field of rational numbers $\mathbb{Q}$, where $a, b, c, d \in \mathbb{Q}$. Let $r_1, r_2, r_3, r_4$ be ...
- 1,037
1
vote
1
answer
122
views
Proving k(α) is a finite extension. [closed]
Let k ⊆ k(α) be a simple extension, with α transcendental over k. Let E be a
subfield of k(α) properly containing k. Prove that k(α) is a finite extension of E.
This is a question from the book "...
- 27