injective hull
Let and be modules.
We say that is an injective hull or injective envelope of
if is both an injective module and an essential extension
of .
Equivalently, is an injective hull of
if is injective,
and is a submodule of ,
and if is a monomorphism
from to an injective module ,
then there exists a monomorphism
such that for all .
Every module has an injective hull, which is unique up to isomorphism. The injective hull of is sometimes denoted .
Title | injective hull |
---|---|
Canonical name | InjectiveHull |
Date of creation | 2013-03-22 12:10:05 |
Last modified on | 2013-03-22 12:10:05 |
Owner | mclase (549) |
Last modified by | mclase (549) |
Numerical id | 7 |
Author | mclase (549) |
Entry type | Definition |
Classification | msc 16D50 |
Synonym | injective envelope |