Characteristic?

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.

Dick

What does the definition of 'ring characteristic' say?

HallsofIvy

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.

matt grime

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

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pivoxa15	Characteristic? Tweet 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.

Dick Recognitions: Homework Help Science Advisor	What does the definition of 'ring characteristic' say?

HallsofIvy Recognitions: Gold Member Science Advisor 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.

matt grime Recognitions: Homework Help Science Advisor	Characteristic? Exercise for the reader: show that the two definitions given are equivalent (in a unital ring).