On Rings with Weakly Prime Centers
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We introduce a class of rings obtained as a generalization of rings with prime centers. A ring R is called weakly prime center (or simply WPC) if ab ϵ Z(R) implies that aRb is an ideal of R, where Z(R) stands for the center of R. The structure and properties of these rings are studied and the relationships between prime center rings, strongly regular rings, and WPC rings are discussed, parallel with the relationship between the WPC and commutativity.
KeywordsLeft Ideal Homomorphic Image Exchange Ring Division Ring Stable Range
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- 4.H. E. Bell and A. Yaqub, “On commutativity of semiperiodic rings,” Result Math., Online First, Birkh¨auser, Doi: 10.1007/s00025-00-0305-5 (2008).