Prove that R is a finitely generated S-module

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R, as a subring of R=ℂ[t] that properly contains ℂ, is shown to be a finitely generated S-module. The discussion revolves around understanding the definition of finitely presented modules and how it applies to this context. Initial confusion is expressed regarding the starting point of the proof, particularly in relation to presentation matrices. Ultimately, clarity is achieved, indicating that the problem is less complex than initially perceived. The conclusion emphasizes the importance of grasping the definitions involved in module theory.
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Homework Statement



Let S be a subring of the ring R=\mathbb{C}[t] which properly contains \mathbb{C}. Prove that R is a finitely generated S-module.

The Attempt at a Solution



Not sure where to start.
 
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Does it have to do with presentation matrices?
 
I would say it has a lot to do with the DEFINITION of "finitely presented module"! How is that defined?
 
I got it. It seemed a lot harder than it is.
 

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