comaximal ideals

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 equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to requiring that there be xI and yJ such that x+y=1.

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

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

Title comaximal ideals
Canonical name ComaximalIdeals
Date of creation 2013-03-22 12:35:57
Last modified on 2013-03-22 12:35:57
Owner yark (2760)
Last modified by yark (2760)
Numerical id 8
Author yark (2760)
Entry type Definition
Classification msc 16D25
Related topic MaximalIdeal
Defines comaximal