-monoid

Module-finite -monoid

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

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

Properties

  1. Finitely generated module over a module-finite -monoid

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

Footnotes

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

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