Finitely generated module

Finitely generated module over a module-finite -monoid

Let be a Module-finite R-monoid and be a finitely generated -module. Then is a finitely generated -module. module

Prove

Let be an -spanning set for and be a -spanning set for . Then

is an -spanning set for , since any may be expressed as an -linear combination of ‘s and the coëfficients may then be expressed as linear combinations of ‘s.

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