Example
Given is the residue class ring
S
=
Z
/
2
Z
[
X
]/(
d
) where
d
=
X
2
+
X
+ 1. A basis for
S
as vector space over
Z
/
2
Z
is 1,
X
,
X
2
. With respect to this basis, multiplication by
X
is a linear map expressed by the matrix
0
0
1
1
0
1
0
1
0
