In
abstract algebra,
ring theory is the study of
rings—
algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the
integers. Ring theory studies the structure of rings, their
representations, or, in different language,
modules, special classes of rings (
group rings,
division rings,
universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as
homological properties and
polynomial identities.