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One forms Ω 1 ( M ) is a module over C ( M ), therefore does that make C ( M ) an algebra or a commutative ring?

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Beginner2022-06-21Added 22 answers

If R is a commutative ring, we say that a commutative ring S equipped with a ring homomorphism R S is an "algebra" over R, or just an R-algebra for brevity.
Thus, there is no inconsistency in saying that C ( M ) is both a commutative ring, and an R-algebra (where R denotes the ring of real numbers, and the homomorphism R C ( M ) sends a real number a to the constant function c a : M R defined by c a ( x ) = a for all x M).

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