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Abstract
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Let R be a ring. The ring R is called weakly prime
center(WPC ring) if ab\in Z(R) implies that aRb is an ideal of
R. In this paper, we prove that every left(right) duo ring is a
WPC ring. Also we prove that some classes of rings with nilpotent
Jacobson radical are WPC rings. Finally, we prove that a simple
ring is a WPC ring if and only if it is a domain
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