hilb-basis.pdf
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THE HILBERT BASIS THEOREM Here is some terminology (which is standard in EGA but less standard in popular commutative algebra books). Let A be a ring (as always, commutative with multi- plicative identity) and fix an A-algebra B. Note that there is an obvious A-module structure on B. We say B is finite over A if the A-algebra B is finitely generated as an A-module. In other words there is a surjective map of A-modules Am −−− B. Here, as always, the two headed right arrow “ ” denotes a surjective map. Am is the direct sum of m-copies of A.…
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