Abstract algebra

The Abstract algebra is the branch of mathematics that deals with various algebraic structures such as groups, rings, objects, modules, and not least the algebras and their properties investigated. The term " abstract " algebra is used for differentiation from other areas of mathematics that are historically conditioned, also referred to as algebra, such as the elementary algebra of school mathematics.

In the history of mathematics, algebraic structures first emerged in other areas of mathematics, were then specified axiomatically, and finally studied as a single entity in abstract algebra. Therefore, the abstract algebra has many links to all branches of mathematics. Through the abstract access can be, for example, parent symmetries discover that then exist in several, actually quite different objects. A modern approach is the category theory. Applications is the abstract algebra, for example, in representation theory or schemes.