If it happens that has an identity element, then is a legitimate element of , and this notation agrees with the usual product of an element and a set.
It is easy to see that for any set which contains .
Applying this first on the right with and then on the left with and , we obtain:
This is called the Peirce Decompostion of with respect to .
This is an example of a generalized matrix ring:
More generally, if has an identity element, and is a complete set of orthogonal idempotents, then
is a generalized matrix ring.
|Date of creation||2013-03-22 14:39:17|
|Last modified on||2013-03-22 14:39:17|
|Last modified by||mclase (549)|