Module

Finitely generated module

An -module is said to be finitely generated iff it has a finite spanning set module so that

Thus a vector space is finitely generate iff it is finite dimensional, however the situation is more complicated over a general ring.

Properties

1. Let , . If and are finitely generated, then so too is .

Proof of 1.

Suppose and . Then

proving ^P1.

Other results

• Finitely generated module over a module-finite R-ring
• Finitely generated modules over a noetherian ring are noetherian (^P2)

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