Affine monoid

In abstract algebra, a branch of mathematics, an affine monoid is a commutative monoid that is finitely generated, and is isomorphic to a submonoid of a free abelian group

[1] Affine monoids are closely connected to convex polyhedra, and their associated algebras are of much use in the algebraic study of these geometric objects.

{\displaystyle (x-y)+(u-v)=(x+u)-(y+v)}

defines the addition.

is integrally closed.