Exchange rings,related comparability and power-substitution

An associative ring R with identity is said to satisfy related comparability provided that for any idempotents e, f ∈ R with e = 1+ ab and f = 1+ba for some a, b ∈R, there exists a central idempotent u ∈R such that ueR is isomorphic to a direct summand of ufR and (1-u)fR is isomorphic to a direct summand of (1 - u)eR In this paper, we investigate the power-cancellation properties of modules over exchange rings satisfying related comparability.