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Local Noetherian Ring

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

#1

Post by Papapetros Vaggelis » 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 \(\displaystyle{m=\langle{x\rangle}}\).
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