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product of ideals
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(Definition)
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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 $AB\subset A\cap B$
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"product of ideals" is owned by mathcam. [ full author list (2) | owner history (1) ]
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Cross-references: contained, sums, ideal generated by, product, ideals, right, ring
There are 10 references to this entry.
This is version 6 of product of ideals, born on 2001-10-20, modified 2008-03-22.
Object id is 411, canonical name is ProductOfIdeals.
Accessed 5832 times total.
Classification:
| AMS MSC: | 16D25 (Associative rings and algebras :: Modules, bimodules and ideals :: Ideals) |
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Pending Errata and Addenda
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