Definition:Lattice (Group Theory)

Definition
Let $n \in \N$ be a natural number.

Let $L$ be a subgroup of the direct product $\displaystyle \Z^n = \prod_{i \mathop = 1}^n \Z$.

Then $L$ is said to be a lattice in $\R^n$ if $\operatorname{span}_{\R} L = \R^n$, i.e. the span of $L$ is $\R^n$.