adjective referring to a mathematical structure in which a certain operation is commutative
In topology, an abelian group is often used to study the fundamental group of a topological space.
In number theory, abelian extensions are extensions of fields that have abelian Galois groups.
In algebra, an abelian group is a group in which the group operation is commutative, meaning that the order of elements does not matter.
In particle physics, abelian gauge theories are theories that involve abelian Lie groups, such as electromagnetism.
In mathematics, the term 'abelian' is used to describe a group or other algebraic structure that satisfies the commutative property, named after the mathematician Niels Henrik Abel.
Physicists may use the term 'abelian' when discussing symmetry in physical systems, particularly in the context of quantum mechanics or field theory.
Chemists may refer to abelian groups in the context of group theory when studying molecular symmetry and bonding.
In computer science, the term 'abelian' may be used in the context of algorithms or data structures that exhibit commutative properties.