Centers and Generalized Centers of Nearrings Without Identity

Abstract

The center of a nearring $N$, in general, is not a subnearring of $N$. The center, however, is contained in a related structure, the generalized center, which is always a subnearring. We give three constructions of nearrings without multiplicative identity and characterize their centers and generalized centers. We find that the centers of these nearrings are always subnearrings.