Correction to Notes on reduced Rickart rings, I. Representation and equational axiomatizations

A reduced Rickart ring is considered as a reduced ring R with an additional operation which associates to every element a∈ R the single idempotent e such that the ideal eR is the right annihilator of a. We discuss some elementary properties of this operation, prove that a ring is reduced and Rickart if and only if it is isomorphic to an associate ring in the sense of I. Sussman (a certain subdirect product of domains with “enough” idempotents), and present several equational axiom systems for reduced Rickart rings.