A slightly
sloppier, although more intuitive notion of characteristic, involves iterating a
ring R's operators using its two
identity elements.
We start off with a
ring's additive
identity 0R. We then add the ring's multiplicative identity
1R to this value. We
iterate the operation over and over, always adding
1R to the previous result.
If we ever reach the ring's additive identity
0R again within a
finite number of steps (call the number
n), we say that the ring has characteristic
n. Otherwise, the ring has characteristic
0.
Thus, the following field stolen from
artermis enteri's writeup on
field:
+ | 0 1 * | 0 1
--+---- --+----
0 | 0 1 0 | 0 0
1 | 1 0 1 | 0 1
has characteristic
2.