Published online by Cambridge University Press: 09 April 2009
It is proved that R is a near-ring with identity in which every element is a power of itself if and only if it is isomorphic with a near-ring of sections of a sheaf of near-fields in which every element is a power of itself. We also obtain that the Boolean spectrum is homeomorphic with the space of all completely prime ideals of R with the Zariski topology.