… Algebraic K-theory has two components: the classical theory which centers around the
Grothendieck group Ko of a category and uses explicit algebraic presentations and higher …

From the Introduction:" These notes are taken from a course on algebraic K-theory [given] at
the University of Chicago in 1967. They also include some material from an earlier course …

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, …
The exposition includes, besides K-theory, a considerable amount of related arithmetic. …

The main result of the paper is in the second part. It says that several definitions of A (X) are
in fact equivalent to each other, up to homotopy. The proof uses most of the results of the first …

… Higher algebraic K-theory: I Daniel Quillen* The purpose of this paper is to develop a higher
K-theory for additive categories with exact sequences which extends the existing theory of …

Algebraic K-Theory has become an increasingly active area of research. With its connections
to algebra, algebraic geometry, topology, and number theory, it has implications for a wide …

… Algebraic K-theory is the branch of algebra dealing with linear algebra (especially in the
limiting … Algebraic K-theory plays an important role in many areas, especially number theory, …

The first section of this paper defines and studies a graded ring K. F associated to any field F.
By definition, K~ F is the target group of the universal n-linear function from F~ x...• F~ to an …

… In this chapter we define and discuss the algebraic K-theory functor. This chapter will mainly
be concerned with the algebraic K-theory of rings, but we will extend this notion at the end of …

… algebraic K-theory are the basic motiviation for this book. We concentrate on developing the
algebra… We reduce the study of RF-modules, their K-theory and homological algebra to the …