Associated graded ring

In mathematics, the associated graded ring of a ring R with respect to a proper ideal I is the graded ring:

\operatorname{gr}_I R = \oplus_{n=0}^\infty I^n/I^{n+1}

.

Similarly, if M is a left R-module, then the associated graded module is the graded module over $\operatorname{gr}_I R$ :

\operatorname{gr}_I M = \oplus_0^\infty I^n M/ I^{n+1} M

.

单词	Associated graded group
释义	Associated graded group 英语百科 Associated graded ring In mathematics, the associated graded ring of a ring R with respect to a proper ideal I is the graded ring: $\operatorname{gr}_I R = \oplus_{n=0}^\infty I^n/I^{n+1}$ . Similarly, if M is a left R-module, then the associated graded module is the graded module over $\operatorname{gr}_I R$ : $\operatorname{gr}_I M = \oplus_0^\infty I^n M/ I^{n+1} M$ .
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Associated graded group