\(K\)-theory of rings with idempotents
type: Item
instance of: scholarly article
title: \(K\)-theory of rings with idempotents
zbMATH Open document ID: 0811.19002
DOI: 10.1007/BF01207710
published in: Mathematical Notes
publication date: 1994-07-13T00:00:00Z
review text: Let \(e\) be some idempotent in a Noetherian ring \(T\). The author proves that there is a long exact sequence \[ \cdots \to K_ *' (eTe/ eT(1 - e)Te) \to K_ *'(T) \to K_ *'((1 - e) T(1 - e)) \to \cdots \] for the \(K\)-theory \(K_ *'\) of finitely generated modules. Under suitable conditions this sequence splits and therefore yields a decomposition of \(K_ *' (T)\). The results are applied to endomorphism rings and graded modules.
Mathematics Subject Classification ID: 19D50
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 567890
zbMATH Keywords: idempotents
zbMATH Keywords: \(K\)-theory
zbMATH Keywords: endomorphism rings
zbMATH Keywords: graded modules
author: Alexei Davydov
reviewed by: Manfred Kolster
MaRDI profile type: Publication
cites work: Group-Graded Rings, Smash Products, and Group Actions
cites work: K i of Upper Triangular Matrix Rings
cites work: Higher algebraic K-theory: I
description: scientific article; zbMATH DE number 567890