A Generalization of p-Rings
نویسنده
چکیده
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 xp = 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 = {0} and Ep = {x ∈ R : xp = x}. With this as motivation, we define a generalized p-ring to be a ring of prime characteristic p such that R \ (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. Mathematics Subject Classification: 16U80, 16D70
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