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.
1
Expert's answer
2013-01-31T08:11:18-0500
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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