Throughout this note A denotes a ring with identity, and “ module ” means “ left unitary module ”. In (2), C. Yohe studied elemental annihilator rings (e.a.r. for brevity). An e.a.r. is defined as a ring in which every ideal is the annihilator of an element of the ring. For example, a semi-simple, Artinian ring is an e.a.r. A is a l.e.a.r. (left elemental annihilator ring) if every left ideal is the left annihilator of an element of the ring. A r.e.a.r. (right elemental annihilator ring) is denned similarly.