International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 667-670
doi:10.1155/S0161171294000943
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
Abstract
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.