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.

Title product of ideals
Canonical name ProductOfIdeals
Date of creation 2013-03-22 11:50:59
Last modified on 2013-03-22 11:50:59
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 11
Author mathcam (2727)
Entry type Definition
Classification msc 16D25
Classification msc 15A15
Classification msc 46L87
Classification msc 55U40
Classification msc 55U35
Classification msc 81R10
Classification msc 46L05
Classification msc 22A22
Classification msc 81R50
Classification msc 18B40
Related topic SumOfIdeals
Related topic QuotientOfIdeals
Related topic PruferRing
Related topic ProductOfLeftAndRightIdeal
Related topic WellDefinednessOfProductOfFinitelyGeneratedIdeals