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### Local Noetherian Ring

Posted: Sun May 29, 2016 2:26 pm
Let $$\displaystyle{\left(A,+,\cdot\right)}$$ be the ring of germs of analytic functions $$\displaystyle{f:\mathbb{R}\to \mathbb{R}}$$

at $$\displaystyle{0\in\mathbb{R}}$$. Then $$\displaystyle{\left(A,+,\cdot\right)}$$ is a $$\displaystyle{\rm{Noethrian}}$$

local ring with maximal ideal $$\displaystyle{m=\langle{x\rangle}}$$.