Abstract
Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring R instead of a field. It associates to any ring R a sequence of abelian groups K n (R). The first two of these groups, K 0 and K 1, are easy to describe in concrete terms. For instance, a finitely generated projective R-module defines an element of K 0(R), and an invertible matrix over R has a “determinant” in K 1(R). The entire sequence of groups K n (R) behaves something like a homology theory of rings.
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Farley, D.S., Ortiz, I.J. (2014). Introduction. In: Algebraic K-theory of Crystallographic Groups. Lecture Notes in Mathematics, vol 2113. Springer, Cham. https://doi.org/10.1007/978-3-319-08153-3_1
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