product of idealsProductOfIdeals2001-10-20 01:57:422008-03-22 21:08:07Definition\usepackage{amssymb}
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\usepackage{xypic}Let $R$ be a ring, and let $A$ and $B$ be left (right) ideals of $R$. Then the {\it 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 $AB\subset A\cap B$.