E-near rings

Abstract.

If R is a left near-ring in which all endomorphisms of R ⁺ are given by¶$a_{\ell} : x \rightarrow ax ({\rm with} \, a, x \in R)$ then (R, +) is shown to be abelian.¶ If also $a_{\ell} = b_{\ell}$ implies a = b, then R is even a ring.