# Answer to Question #23252 in Abstract Algebra 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.
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