Examples
We come back to the examples of the definition in Section 7.3.
Usual arithmetic
Modular arithmetic
fields of rational functions
Residue class fields
The Gaussian numbers
The characteristic of R = Q, R, C, or any subfield of
C is 0.
Of course, Z/pZ has characteristic p.
If R is a field,
the characteristic of the
field of rational functions
R(X) is equal to the characteristic of
R.
If R is a field and
f an irreducible polynomial in R[X] of positive degree,
then the residue class ring
R[X]/(f) is a field whose characteristic is that of R.
The characteristic of Q+Qi is 0.