Coprime: Difference between revisions
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More generally, in [[ring theory]], two elements of a ring are coprime if the only elements of the ring which divide both of them are [[unit]]s. Two ideals are coprime if the smallest ideal that contains them both is the ring itself. | More generally, in [[ring theory]], two elements of a ring are coprime if the only elements of the ring which divide both of them are [[unit]]s. Two ideals are coprime if the smallest ideal that contains them both is the ring itself. | ||
==See also== | |||
* [[Highest common factor]] | |||
Revision as of 02:27, 30 October 2008
In arithmetic, two integers are coprime if they have no common factor greater than one.
More generally, in ring theory, two elements of a ring are coprime if the only elements of the ring which divide both of them are units. Two ideals are coprime if the smallest ideal that contains them both is the ring itself.