2010/09/16 by Chenghao Chu, Chu, Chenghao, Jack Morava +1
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT
paper · pdf · doi:10.48550/arxiv.1009.3235
arxiv created 2010/09/16 · arxiv updated 2010/09/17
Let A be a not necessarily commutative monoid with zero such that projective A-acts are free. This paper shows that the algebraic K-groups of A can be defined using the +-construction and the Q-construction. It is shown that these two constructions give the same K-groups. As an immediate application, the homotopy invariance of algebraic K-theory of certain affine \mathbbF1-schemes is obtained. From the computation of K2(A), where A is the monoid associated to a finitely generated abelian group, the universal central extension of certain groups are constructed.