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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