Abstract Algebra: Theory and Applications · Problem 20.2

Fields — Thomas Judson

Mathematics — Abstract Algebra · vector-spaces-subspaces

Problem

The set

V = \mathbb{Q}(\sqrt{11}) = \{a + b\sqrt{11} \mid a, b \in \mathbb{Q}\}

is a vector space. Carefully define the operations on this set that will make this possible. Describe the subspace spanned by

S = \{\mathbf{u}\}

, where

\mathbf{u} = 3 + \frac{2}{7}\sqrt{11} \in V