---
tag: 4GV4XB7EVM
kind: concept
name: Affine monoid
sources:
  - wikipedia: en:42069780@r1367653080
    locator: Affine monoid
    note: adopted
    mention: wikipedia://en/42069780
    sections: [Summary]
same_as:
  wikidata: Q17003488
  wikipedia: Affine monoid
inventory: [SH0DPQ2T7Z]
---

## Summary

In abstract algebra, a branch of mathematics, an **affine monoid** is a commutative [[monoid|0N6R902FG1]] that is finitely generated, and is isomorphic to a submonoid of a [[free abelian group|0WJX8MGG37]] $\mathbb{Z}^d, d \ge 0$. Affine monoids are closely connected to convex polyhedra, and their associated algebras are of much use in the algebraic study of these geometric objects.