ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11780 on D174: Vector space dimension
F11780
Formulation 1
Let $R$ be a D273: Division ring such that
(i) $V$ is a D29: Vector space over $R$
(ii) $B$ is a D173: Vector space basis for $V$ over $R$
The dimension of $V$ over $R$ is the D15: Set cardinality \begin{equation} \text{dim}_R(V) : = |B| \end{equation}