# Answer to Question #23251 in Abstract Algebra for Hym@n B@ss

Question #23251

Show that the center Z(R) of prime ring R is an integral domain, and char R is either 0 or a prime number.

Expert's answer

Let nonzero

*a**∈**Z*(*R*), and say*ab*= 0. Then*aRb*=*Rab*= 0, so*b*= 0 since*R*is a prime ring. This says that*a*is not a zero-divisor in*R*, and for domains char*R*is either0 or a prime number.
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