Perfect ideal
id:
perfect-ideal-248-12431374
title:
Perfect ideal
text:
In commutative algebra, a perfect ideal is a proper ideal I in a Noetherian ring R such that its grade equals the projective dimension of the associated quotient ring. grade = proj dim . A perfect ideal is unmixed. For a regular local ring R a prime ideal I is perfect if and only if R / I is Cohen-Macaulay. The notion of perfect ideal was introduced in 1913 by Francis Sowerby Macaulay in connection to what nowadays is called a Cohen-Macaulay ring, but for which Macaulay did not have a name for
brand slug:
wiki
category slug:
encyclopedia
description:
A type of ideal relevant for Noetherian rings
original url:
https://en.wikipedia.org/wiki/Perfect_ideal
date created:
date modified:
2024-01-30T09:56:32Z
main entity:
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image:
fields total:
13
integrity:
14