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principal ideal (Definition)

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)$.



"principal ideal" is owned by djao.
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Cross-references: commutative ring, ideal, right, ring
There are 28 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 4828 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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