Characteristic of a ring

The characteristic of a ring is the number of times you must add the multiplicative identity element in order to get the additive identity element.

If adding the multiplicative identity element to itself, no matter how many times, never gives us the additive identity element, we say the characteristic is 0. Otherwise, there must exist an integer p such that p × n = 0 for all n. The value of p is then the characteristic of the ring.

In a ring of characteristic 2, the elements 2, 4, etc., are all equal to 0. In a ring of characteristic 3, the elements 3, 6, etc., are all equal to 0.

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