PlanetMath: dense ideals/subsets of a ring

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dense ideals/subsets of a ring

(Definition)

Given a commutative ring , 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:

16D25 (Associative rings and algebras :: Modules, bimodules and ideals :: Ideals)

Pending Errata and Addenda

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