R-monoid

Module-finite 𝑅-monoid

An 𝑅-monoid (or ring extension) 𝑇 is called module-finite¹ iff 𝑇 is finitely generated as an 𝑅-module, ring i.e. there exists an onto 𝑅-module homomorphism

𝑅(𝑛)↠𝑇

for some 𝑛 ∈ℕ0. This should not be confused with the weaker condition of R-monoid of finite type.²

Properties

1. Finitely generated module over a module-finite R-ring

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Footnotes

1. The usual terminology is just finite, but I find this misleading. ↩

2. 2009. Algebra: Chapter 0, §III.6.5, p. 171 ↩