System of parameters
id:
system-of-parameters-258-18370392
title:
System of parameters
text:
In mathematics, a system of parameters for a local Noetherian ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions: m is a minimal prime over (x1, ..., xd).
The radical of (x1, ..., xd) is m.
Some power of m is contained in (x1, ..., xd).
(x1, ..., xd) is m-primary. Every local Noetherian ring admits a system of parameters. It is not possible for fewer than d elements to generate an ideal whose radical is m beca
brand slug:
wiki
category slug:
encyclopedia
description:
Mathematical concept in dimension theory of local rings
original url:
https://en.wikipedia.org/wiki/System_of_parameters
date created:
date modified:
2023-08-22T03:37:15Z
main entity:
{"identifier":"Q7663733","url":"https://www.wikidata.org/entity/Q7663733"}
image:
fields total:
13
integrity:
14