stable isomorphism

Let R be a ring with unity 1. Two left R-modules M and N are said to be stably isomorphic if there exists a finitely generatedMathworldPlanetmathPlanetmath free R-module Rn (n1) such that


A left R-module is said to be stably free if it is stably isomorphic to a finitely generated free R-module. In other words, M is stably free if


for some positive integers m,n.

Remark In the Grothendieck group K0(R) of a ring R with 1, two finitely generated projective module representatives M and N such that [M]=[N]K0(R) iff they are stably isomorphic to each other. In particular, [M] is the zero elementMathworldPlanetmath in K0(R) iff it is stably free.

Title stable isomorphism
Canonical name StableIsomorphism
Date of creation 2013-03-22 15:00:00
Last modified on 2013-03-22 15:00:00
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 4
Author CWoo (3771)
Entry type Definition
Classification msc 19A13
Related topic AlgebraicKTheory
Defines stably isomorphic
Defines stably free