Noetherian property of inductive limits of noetherian local rings
Copyright policy )Noetherian property of inductive limits of noetherian local rings
This note is concerned with verifying the following result. Let \(\{(A_ i,m_ i)\mid i\) is an element of \(I\)\} be a filtered inductive system of noetherian local rings such that \(m_ iA_ j=m_ j\) for \(j\geq i\). Then the inductive limit \(A\) of the system is noetherian.
filtered inductive system, inductive limit, Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.), noetherianness, 13E05, Commutative Noetherian rings and modules, 13B99, Local rings and semilocal rings
filtered inductive system, inductive limit, Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.), noetherianness, 13E05, Commutative Noetherian rings and modules, 13B99, Local rings and semilocal rings
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