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comaximal ideals (Definition)

Let $ R$ be a ring.

Two ideals $ I$ and $ J$ of $ R$ are said to be comaximal if $ I + J = R$. If $ R$ is unital, this is equivalent to requiring that there be $ x\in I$ and $ y\in J$ such that $ x+y=1$.

For example, any two distinct maximal ideals of $ R$ are comaximal.

A set $ \cal S$ of ideals of $ R$ is said to be pairwise comaximal (or just comaximal) if $ I+J=R$ for all distinct $ I,J\in\cal S$.



"comaximal ideals" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: maximal ideal

Also defines:  comaximal
Keywords:  comaximal

Attachments:
pairwise comaximal ideals property (Result) by polarbear
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Cross-references: maximal ideals, ideals, ring
There are 3 references to this entry.

This is version 5 of comaximal ideals, born on 2002-04-19, modified 2006-09-09.
Object id is 2851, canonical name is Comaximal.
Accessed 2804 times total.

Classification:
AMS MSC: 16D25 (Associative rings and algebras :: Modules, bimodules and ideals :: Ideals)
Pending Errata and Addenda
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