Structure of rings with certain conditions on zero divisors

Abstract

LetRbe a ring such that every zero divisorxis expressible as a sum of a nilpotent element and a potent element ofR:x=a+b, whereais nilpotent,bis potent, andab=ba. We call such a ring aD*-ring. We give the structure of periodicD*-ring, weakly periodicD*-ring, ArtinianD*-ring, semiperfectD*-ring, and other classes ofD*-ring.