Basic elements: Theorems from algebraic $K$-theory

Basic Elements: Theorems from Algebraic Avtheory

Generating Modules Efficiently: Theorems from Algebraic K-Theory

Several of the fundamental theorems about algebraic K, and Kr are concerned with finding unimodular elements, that is, elements of a projective module which generate a free summand. In this paper we use the notion of a basic element (in the terminology of Swan [22]) to extend these theorems to the context of finitely generated modules. Our techniques allow a simplification and strengthening of ...

Algebraic proofs of some fundamental theorems in algebraic K - theory

We present new proofs of the additivity, resolution and cofinality theorems for the algebraic K-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic K-groups via binary complexes. 2000 Mathematics Subject Classification: 19D99

Bivariant algebraic K-theory

We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive Ktheory of algebras over a fixed unital ground ring H, (A, B) 7→ kk∗(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel’s homotopy algebraic K-theory, KH....

Algebraic K - Theory

We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive Ktheory of algebras over a fixed unital ground ring H, (A, B) 7→ kk∗(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel’s homotopy algebraic K-theory, KH....