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dense ideals/subsets of a ring (Definition)

Given a commutative ring $ R$, an ideal/subset $ I\subset R$ is said to be dense iff its annihilator is $ \{0\}$, in other words

$\displaystyle \mathrm{Ann}(I)=\{0\}$

We can similarly define right dense and left dense in the case of noncommutative rings.



"dense ideals/subsets of a ring" is owned by jocaps.
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Also defines:  dense subset of a ring, dense ideals
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Cross-references: rings, noncommutative, annihilator, iff, ideal, commutative ring
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This is version 9 of dense ideals/subsets of a ring, born on 2006-10-29, modified 2006-11-05.
Object id is 8491, canonical name is DenseIdealssubsetsOfARing.
Accessed 1313 times total.

Classification:
AMS MSC16D25 (Associative rings and algebras :: Modules, bimodules and ideals :: Ideals)

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