algebraic K-theory

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological and algebraic. Topological K-theory is the "true" K-theory in the sense that it came first. Topological K-theory has to do with vector bundles over topological spaces. Elements of a K-theory are stable equivalence classes of vector bundles over a topological space. You can put a ring structure on the collection of stably equivalent bundles by defining addition through the Whitney sum, and multiplication through the tensor product of vector bundles. This defines "the reduced real topological K-theory of a space."