In [1] L. Fuchs and I. Halperin have proved that a regular ring R is isomorphic to a two-sided ideal of a regular ring with identity. ([1] Theorem 1). Their methed is to imbed the regular ring R in the ring of all pairs (a, p) with a ∊ R and p from a suitable commutative regular ring S with identity such that R is an algebra over S. Thus S may be seen as the ring of R — R endomorphisms of the additive group of R. The following question is naturally raised: Is it true that the ring of all R-R endomorphisms of a rugular ring is a commutative regular ring? The main purpose of this paper is to answer this question affirmatively. (Theorem 1). After established this theorem we can follow the method in [1] to solve the problem in the title.