Near-rings whose group of units acts fixedpointfree
by
Gerhard Wendt
Johannes Kepler Universität Linz

Given a near-ring (N, +, *) with identity (group operation + is not necessarily abelian, multiplication * is only satisfying the right distributivity law) one can consider the right translation maps n → n*u (n an element of N, u an invertible element in N w.r.t. *). These maps are automorphisms of the group (N, +). In case N is a near-field, all these right translation maps are automorphisms without a non-trivial fixed point. But there is another class of near-rings satisfying this property. We introduce this type of near-rings and discuss some of its properties.

Date received: May 15, 2008