R-monoid of finite type

Commutative -monoid of finite type

A Commutative R-monoid being of finite type is equivalent to the existence of an -monoid homomorphism calg

from the polynomial ring in indeterminates.

Proof

Noting that the polynomial ring is the “abelianization” of the Free R-ring, this follows from the characterization of a general R-monoid of finite type.

As such, these are just quotients of the polynomial ring.

Properties

• Hilbert’s basis theorem

---

develop | en | sembr