Radicals and idempotents III: Q -central idempotents

Abstract

Previously ['Radicals and idempotents I, II', Comm. Alg. 49(1) (2021), 73-84 and 50(11) (2022), 4791-4804], we have studied the interaction between radicals of rings and idempotents in general or those of particular types, for example, left semicentral. Here we carry out similar investigations for q-central idempotents, that is, those idempotents e satisfying the condition (ea-eae)(be-ebe) = 0 for all a, b.