Algebraic K-theory of rings

The topic of this seminar will be the algebraic K-theory. This week we'll give an overview of the construction of K-groups for the case of rings. These include the group K_0(R) of a ring, which can be thought of as the generalization of dimensions for vector spaces, the infinite general linear group GL(R) and K_1(R), and the Steinberg group St(R) and K_2(R). Additionally, there will be many examples in ring and number theory to help illustrate where such concepts might naturally arise. Next week we'll go about rigorously constructing the zeroth K-group group K_0(M) for a monoid M.