stable isomorphism
Let be a ring with unity 1. Two left -modules and
are said to be stably isomorphic if there exists a finitely
generated free -module () such that
A left -module is said to be stably free if it is stably isomorphic to a finitely generated free -module. In other words, is stably free if
for some positive integers .
Remark In the Grothendieck group of a ring
with 1, two finitely generated projective module representatives
and such that iff they are stably isomorphic
to each other. In particular, is the zero element in
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 |