abstract algebra

To a mathematician, real life is a special case.

Abstract algebra is algebra that is not confined to familiar number systems, such as the real numbers, but seeks to solve equations that may involve many other kinds of system. One of its aims, in fact, is to ask: what other number systems are there? The term "abstract" refers to the perspective taken in the subject, which is very different from that of high school algebra. Rather than looking for the solutions to a particular problem, abstract algebra is interested in such questions as: When does a solution exist? If a solution does exist, is it unique? What general properties does a solution possess? Among the structures it deals with are groups, rings, and fields. Historically, examples of such structures often arose first in some other field of mathematics, were specified rigorously (axiomatically), and were then studied in their own right in abstract algebra.