conjugate module
If is a right module over a ring ,
and is an endomorphism of ,
we define the conjugate module
to be the right -module
whose underlying set is ,
with abelian group
structure
identical to that of
(i.e. ),
and scalar multiplication given by
for all in and in .
In other words, if
is the ring homomorphism that describes
the right module action of upon ,
then describes
the right module action of upon .
If is a left -module, we define similarly, with .
Title | conjugate module |
---|---|
Canonical name | ConjugateModule |
Date of creation | 2013-03-22 11:49:47 |
Last modified on | 2013-03-22 11:49:47 |
Owner | antizeus (11) |
Last modified by | antizeus (11) |
Numerical id | 9 |
Author | antizeus (11) |
Entry type | Definition |
Classification | msc 16D10 |
Classification | msc 41A45 |