Abstract Algebra: Theory and Applications · Problem 21.5.9

Finite Fields — Thomas Judson

Mathematics — Abstract Algebra · algebraic-extension-not-finite

Problem

Prove that Q(3,34,38,…)\mathbb{Q}(\sqrt{3}, \sqrt[4]{3}, \sqrt[8]{3}, \ldots) is an algebraic extension of Q\mathbb{Q} but not a finite extension.

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