Module-finite $K$ -monoid

An $K$ -monoid (or ring extension) $𝑇$ is called module-finite¹ iff $𝑇$ is finitely generated as an $K$ -module, #m/def/ring i.e. there exists an onto $K$ -module homomorphism

K (𝑛) ↠ 𝑇

for some $𝑛 \in ℕ 0$ . This should not be confused with the weaker condition of $K$ -monoid of finite type.²

Properties

Finitely generated module over a module-finite $K$ -monoid

#state/tidy | #lang/en | #SemBr

The usual terminology is just finite, but I find this misleading. ↩
2009. Algebra: Chapter 0, §III.6.5, p. 171 ↩