Abstract
Let R be a ring with Jacobson ideal J and center C. McCoy and Montgomery introduced the concept of a p-ring (p prime) as a ring R of characteristic p such that x p = x for all x in R. Thus, Boolean rings are simply 2-rings (p = 2). It readily follows that a p-ring (p prime) is simply a ring R of prime characteristic p such that R N + Ep, where N = f0g and Ep = fx 2 R : x p = xg. With this as motivation, we dene a generalized p-ring to be a ring of prime characteristic p such that Rn (J[ C) N + Ep, where N denotes the set of nilpotents of R (and Ep is as above). The commutativity behavior of these rings is considered.
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