R-monoid of finite type

Commutative 𝑅-monoid of finite type

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

𝑅[𝑥1,…,𝑥𝑛]↠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 R-monoid of finite type.

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

Properties

• Hilbert’s basis theorem

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