On distributively generated near-rings

Abstract

The following theorems in ring theory are well-known: 1. Let R be a ring. If e is a unique left identity, then e is also a right identity. 2. If R is a ring with more than one element such that aR = R for every nonzero element a ε R , then R is a division ring. 3. A ring R with identity e ≠ 0 is a division ring if and only if it has no proper right ideals.