Characteristic of R is a Divisor of |R| (Modern Algebra)

[FanofAFan]

Homework Statement

if R is a finite ring, then the characteristic of R is a divisor of | R |.

Homework Equations

The Attempt at a Solution

Can this be proven using lagrange's and char R is the subgroup and R is finite group, then the order of char R is a divisor order of R, and i use coset to show this? or am I completely off thanks

 

[Dick]

Homework Statement

if R is a finite ring, then the characteristic of R is a divisor of | R |.

Homework Equations

The Attempt at a Solution

Can this be proven using lagrange's and char R is the subgroup and R is finite group, then the order of char R is a divisor order of R, and i use coset to show this? or am I completely off thanks

That's pretty much it, yes. The ring R under addition is a group. The characteristic of R is the size of the subgroup of R.