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Local Noetherian Ring

Linear Algebra, Algebraic structures (Groups, Rings, Modules, etc), Galois theory, Homological Algebra
Papapetros Vaggelis
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Local Noetherian Ring

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 $\displaystyle{m=\langle{x\rangle}}$.