# What is the definition of a characteristic of a ring?

1. Mar 28, 2007

### pivoxa15

What is the definition of a characteristic of a ring?

Is it the smallest n such that n1=0? or is it the smallest n such that nr=0 for all r in R.

2. Mar 28, 2007

### Dick

What does the definition of 'ring characteristic' say?

3. Mar 28, 2007

### HallsofIvy

Staff Emeritus
Copied from Wikipedia:

In mathematics, the characteristic of a ring R with multiplicative identity element 1R is defined to be the smallest positive integer n such that

n1R = 0,
where n1R is defined as

1R + ... + 1R with n summands.

4. Mar 28, 2007

### matt grime

Exercise for the reader: show that the two definitions given are equivalent (in a unital ring).