Editing Lattice (group) (section)

==Lattices in complex space==
A lattice in <math>\mathbb{C}^n</math> is a discrete subgroup of <math>\mathbb{C}^n</math> which spans <math>\mathbb C^n</math> as a real vector space. As the dimension of <math>\mathbb C^n</math> as a real vector space is equal to <math>2n</math>, a lattice in <math>\mathbb{C}^n</math> will be a free abelian group of rank <math>2n</math>.

For example, the [[Gaussian integer]]s <math>\mathbb Z[i] = \mathbb Z + i\mathbb Z</math> form a lattice in <math>\mathbb C = \mathbb{C}^1</math>, as <math>(1, i)</math> is a basis of <math>\mathbb C</math> over <math>\mathbb R</math>.