Definition
abelian
adjective
- of or relating to a group in which the result of combining any two elements does not depend on the order in which they are combined; commutative
Usage: mathematics; named after Norwegian mathematician Niels Henrik Abel
Examples
- The integers under addition form an abelian group.
- In an abelian group, a + b equals b + a for all elements a and b.
- The multiplicative group of non-zero real numbers is abelian.
- Abelian groups are fundamental structures in abstract algebra.
- Unlike some matrix groups, the group of rotations in three dimensions is non-abelian, not abelian.