A.BENINI and F.MORINI

Weakly divisible nearrings on the group of integers

Pages: 1-11
Received: 16 March 1998   
Mathematics Subject Classification (2000): 16Y30

Abstract: A nearring N is weakly divisible (wd-nearring) if, for each x,y of N, there exists an element z of N such that xz = y or yz = x. In this paper we characterise and construct all zerosymmetric wd-nearrings on the group (Z_pⁿ, +) of integers (mod pⁿ), p prime, in which pZ_pⁿ is the set of all the nilpotent elements.