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单词 ProductOfIdeals
释义

product of ideals


Let R be a ring, and let A and B be left (right) ideals of R. Then the product of the ideals A and B, which we denote AB, is the left (right) ideal generated byPlanetmathPlanetmath all products ab with aA and bB. Note that since sums of products of the form ab with aA and bB are contained simultaneously in both A and B, we have ABAB.

Titleproduct of ideals
Canonical nameProductOfIdeals
Date of creation2013-03-22 11:50:59
Last modified on2013-03-22 11:50:59
Ownermathcam (2727)
Last modified bymathcam (2727)
Numerical id11
Authormathcam (2727)
Entry typeDefinition
Classificationmsc 16D25
Classificationmsc 15A15
Classificationmsc 46L87
Classificationmsc 55U40
Classificationmsc 55U35
Classificationmsc 81R10
Classificationmsc 46L05
Classificationmsc 22A22
Classificationmsc 81R50
Classificationmsc 18B40
Related topicSumOfIdeals
Related topicQuotientOfIdeals
Related topicPruferRing
Related topicProductOfLeftAndRightIdeal
Related topicWellDefinednessOfProductOfFinitelyGeneratedIdeals
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更新时间:2025/5/4 9:23:34