A. BENINI and F. MORINI
On the construction of a class of weakly divisible nearrings
Received: 5 May 1998
Mathematics Subject Classification (2000): 16Y30
Work carried out on behalf of Italian M.U.R.S.T.
Abstract: A nearring N is called weakly divisible (wd-nearring) if, for each x,y included in N, there exists an element z in N such that xz=y or yz=x. A method to generate all the zerosymmetric wd-nearrings on the cyclic group (Zpn, +) whose set of the nilpotent elements equals pZpn is already known. In this paper we give an account of the orbits of a subgroup of the automorphism group of (Zpn, +) to provide the guide for improving the construction method of such wd-nearrings.