Algebraic K -theory of Parameterized Endomorphisms

Assume that M is an R-bimodule. Let End(R,M) denotes the category whose objects are pairs (P,f ), where P is a finitely generated projective right R-module and f :P →P ⊗M. It has an exact structure obtained from the category of projectives over R by forgetting fs. We prove that, when R is a field, we have K(End(R,M))=ωKσ−1TM denotes certain localization of the tensor algebra spanned by M. This result should be viewed as a special case of the noncommutative extension of the results of [4].