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principal ideal
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(Definition)
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Let $R$ be a ring and let $a \in R$ The principal left (resp. right, 2-sided) ideal of $a$ is the smallest left (resp. right, 2-sided) ideal of $R$ containing the element $a$
When $R$ is a commutative ring, the principal ideal of $a$ is denoted $(a)$
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"principal ideal" is owned by djao.
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Cross-references: commutative ring, ideal, right, ring
There are 34 references to this entry.
This is version 2 of principal ideal, born on 2001-10-21, modified 2002-10-24.
Object id is 437, canonical name is PrincipalIdeal.
Accessed 6451 times total.
Classification:
| AMS MSC: | 13A15 (Commutative rings and algebras :: General commutative ring theory :: Ideals; multiplicative ideal theory) | | | 16D25 (Associative rings and algebras :: Modules, bimodules and ideals :: Ideals) |
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Pending Errata and Addenda
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