Commutative $K$ -monoid of finite type

A commutative $K$ -monoid $𝑇$ being of finite type is equivalent to the existence of an $K$ -monoid homomorphism #m/thm/calg

K [𝑥 1, \dots, 𝑥 𝑛] ↠ 𝑇

from the polynomial ring in $𝑛$ indeterminates.

Proof

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

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

Properties

Hilbert's basis theorem

#state/develop | #lang/en | #SemBr

Commutative K-monoid of finite type

Properties

Commutative $K$ -monoid of finite type