Center--like subsets in rings with derivations or epimorphisms

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Brock University‎, ‎St‎. ‎Catharines‎, ‎Ontario L2S 3A1‎, ‎Canada.

2 Department of Mathematics‎, ‎Al-Azhar University‎, ‎Nasr City(11884)‎, ‎Cairo‎, ‎Egypt.

Abstract

We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.

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