Involution near-rings

Abstract

Throughout this paper all near-rings considered will be zero-symmetric and left distributive. All groups will be written additively, but this does not imply commutativity. The near-ring of all zero-fixing maps of a group V into itself will be denoted by Mo(V). If N is a near-ring withan identity and α ≠ 1 is an element of N such that α2 = 1, then α will be called an involution of N. Let V be a group. An involution a of Mo(V) will be called an involution on V.