Lattice (module)

In mathematics, particularly in the field of ring theory, a lattice is an algebraic structure which, informally, provides a general framework for taking a sparse set of points in a larger space. Lattices generalize several more specific notions, including integer lattices in real vector spaces, orders in algebraic number fields, and fractional ideals in integral domains. Formally, a lattice is a kind of module over a ring that is embedded in a vector space over a field.