<sod>  
 If the ideals ''A'' and ''B'' of ''R'' are coprime, then ''AB'' = ''A''&cap;''B''; furthermore, if ''C'' is a third ideal such that ''A'' contains ''BC'', then ''A'' contains ''C''. The [[Chinese Remainder Theorem]] is an important statement about coprime ideals.
 
The concept of being ''relatively prime'' can also be extended any [[finite]] [[set]] of integers (''S'' = {''a''<sub>1</sub>, ''a''<sub>2</sub>, .... ''a''<sub>''n''</sub>}) to mean that  the [[greatest common divisor]] of the elements of the set is 1. If there does not exist any relatively prime pair of integers in the set, then the set is called ''pairwise relatively prime''. Every pairwise relatively prime set is relative prime; however, the converse is not true: {6, 10, 15} is relatively prime, but not pairwise relative prime.
 
 ==See also==
 
 <eod> <sod> 
 If the ideals ''A'' and ''B'' of ''R'' are coprime, then ''AB'' = ''A''&cap;''B''; furthermore, if ''C'' is a third ideal such that ''A'' contains ''BC'', then ''A'' contains ''C''. The [[Chinese Remainder Theorem]] is an important statement about coprime ideals.
 
The concept of being ''relatively prime'' can also be extended any [[finite]] [[set]] of integers ''S'' = {''a''<sub>1</sub>, ''a''<sub>2</sub>, .... ''a''<sub>''n''</sub>} to mean that the [[greatest common divisor]] of the elements of the set is 1. If every ''pair'' of integers in the set is relatively prime, then the set is called ''pairwise relatively prime''.

Every pairwise relatively prime set is relative prime; however, the converse is not true: {6, 10, 15} is relatively prime, but not pairwise relative prime.
 
 ==See also==
 
 <eod>