Affine monoids and their Hilbert bases

Affine monoids are the basic structure on which algebras with coefficients in rings will be built later on. Their finiteness properties allow a rich structure theory, both from the combinatorial and the ring theoretic point of view to be pursued in later chapters. An affine monoid defines a cone in a natural way, and therefore the notions of polyhedral convex geometry will be omnipresent in this chapter.