[[R-monoid]]
# $R$-monoid of finite type

An $R$-monoid (or [[ring extension]]) $T$ is called **of finite type** iff it has finitely many generators, as an $R$-monoid, #m/def/ring
or equivalently there exists an onto $R$-monoid homomorphism
$$
\begin{align*}
R \langle x_{1},\dots,x_{n} \rangle \twoheadrightarrow T
\end{align*}
$$
from the [[Free R-monoid]].
In particular, see the special case of [[Commutative R-monoid of finite type]].

## See also

- [[Finitely generated field extension]]

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