Graded Nakayama's lemma: Difference between revisions
(New page: {{indispensable lemma}} ==Statement== Suppose <math>A</math> is a graded ring. Let <math>A^+</math> denote the ideal of all positively graded elements. Then, if <math>M</math> is an ...) |
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Suppose <math>A</math> is a [[graded ring]]. Let <math>A^+</math> denote the ideal of all positively graded elements. Then, if <math>M</math> is an <math>A</math>-[[graded module]], <math>A^+M = M \implies M = 0</math>. | Suppose <math>A</math> is a [[graded ring]]. Let <math>A^+</math> denote the ideal of all positively graded elements. Then, if <math>M</math> is an <math>A</math>-[[graded module]], <math>A^+M = M \implies M = 0</math>. | ||
==Related results== | |||
* [[Nakayama's lemma]] | |||
Revision as of 21:27, 8 February 2008
This article is about the statement of a simple but indispensable lemma in commutative algebra
View other indispensable lemmata
Statement
Suppose is a graded ring. Let denote the ideal of all positively graded elements. Then, if is an -graded module, .