Dimension of direct product is sum of dimensions

The statement could be used in a wide variety of contexts:

Context of additional structure on group	Notion of dimension	Statement
real Lie group	dimension of a real Lie group	dimension of direct product of real Lie groups is sum of dimensions
complex Lie group	dimension of a complex Lie group	dimension of direct product of complex Lie groups is sum of dimensions
algebraic group	dimension of an algebraic group	dimension of direct product of algebraic groups is sum of dimensions