A. BENINI and F. MORINI

On the construction of a class of weakly divisible nearrings

Pages: 103-111
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 (Z_pⁿ, +) whose set of the nilpotent elements equals pZ_pⁿ is already known. In this paper we give an account of the orbits of a subgroup of the automorphism group of (Z_pⁿ, +) to provide the guide for improving the construction method of such wd-nearrings.