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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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