Grade (ring theory)
id:
grade-ring-theory-264-18269342
title:
Grade (ring theory)
text:
In commutative and homological algebra, the grade of a finitely generated module M over a Noetherian ring R is a cohomological invariant defined by vanishing of Ext-modules grade M = grade R M = inf { i ∈ N 0 : Ext R i ≠ 0 } . For an ideal I ◃ R the grade is defined via the quotient ring viewed as a module over R grade I = grade R I = grade R R / I = inf { i ∈ N 0 : Ext R i ≠ 0 } . The grade is used to define perfect ideals. In general we have the inequality grade R I ≤ proj dim where the proj
brand slug:
wiki
category slug:
encyclopedia
description:
Invariant for finitely generated modules over a Noetherian ring
original url:
https://en.wikipedia.org/wiki/Grade_(ring_theory)
date created:
date modified:
2024-03-26T01:02:19Z
main entity:
{"identifier":"Q121733921","url":"https://www.wikidata.org/entity/Q121733921"}
image:
fields total:
13
integrity:
14