# 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 by all products $ab$ with $a\in A$ and $b\in B$. Note that since sums of products of the form $ab$ with $a\in A$ and $b\in B$ are contained simultaneously in both $A$ and $B$, we have $AB\subset A\cap B$.

 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