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It is part of an exercise in the book Basic Homological Algebra, Chapter 2 Exercise 16.

Suppose $R$ is the subring of $C^\infty(\mathbb{R})$ of all functions with period $2\pi$, and let $I$ be the maximal ideal of $R$ consisting of all functions of $R$ taking $0$ to $0$.

How can I prove that $I$ is generated by $\sin(x)$ and any (one) function in $I$ which take nonzero value at $\pi$?

  • 0
    Would Fourier series help?2012-07-11
  • 0
    given a fctn in I use the 'any (one) function' to make it also vanish at $\pi$, then divide by sin2012-07-11

1 Answers 1