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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 ais not a zero-divisor in R, and for domains char R is either0 or a prime number.

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