# Answer on Abstract Algebra Question for Hym@n B@ss

Question #23252

For any semiprime ring R, show that Z(R) is reduced, and that char R is either 0 or a square-free integer.

Expert's answer

Let

*a**∈**Z*(*R*) be such that*a^*2 = 0. Then*aRa*=*Ra^*2 = 0, so*a*= 0. This shows that*Z*(*R*) is areduced (commutative) ring, and then char*R*is either 0 or a square-freeinteger.Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment