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Topics: Abstract Algebra - Ring Theory
Ring Theory
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.
For our universe we take the set of all rings. Some are commutative, some have unity, some are/have both. Some commutative rings with unity have zero divisors, some do not; those that do not are called integral domains. Some integral domains are fields. (Source: https://rip94550.wordpress.com/2012/07/02/introduction-to-rings/)
