International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 667-670

On rings with prime centers

Hazar Abu-Khuzam1 and Adil Yaqub2

1Department of Mathematics, American University of Beirut, Beirut, Lebanon
2Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California, USA

Received 4 December 1992; Revised 26 June 1993

Copyright © 1994 Hazar Abu-Khuzam and Adil Yaqub. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of prime centers to commutativity. An example of a non-commutative ring with a prime center is given.