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primitive ideal
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(Definition)
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Let $R$ be a ring, and let $I$ be an ideal of $R$ . We say that $I$ is a left (right) primitive ideal if there exists a simple left (right) $R$ -module $X$ such that $I$ is the annihilator of $X$ in $R$ .
We say that $R$ is a left (right) primitive ring if the zero ideal is a left (right) primitive ideal of $R$ .
Note that $I$ is a left (right) primitive ideal if and only if $R/I$ is a left (right) primitive ring.
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"primitive ideal" is owned by antizeus.
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(view preamble | get metadata)
| Other names: |
primitive ring |
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Cross-references: zero ideal, annihilator, simple, right, ideal, ring
There are 5 references to this entry.
This is version 2 of primitive ideal, born on 2001-11-24, modified 2002-10-25.
Object id is 1007, canonical name is PrimitiveIdeal.
Accessed 4956 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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