Extensions of reversible rings

A ring R is called reversible if ab=0 implies ba=0 for a,b R. We continue in this paper the study of reversible rings by Cohn [4]. We first consider properties and basic extensions of reversible rings and related concepts to reversible rings, including some kinds of examples needed in the process. We next show that polynomial rings over reversible rings need not be reversible, and sequentially argue about the reversibility of some kinds of polynomial rings. Moreover we prove that if R is a reduced ring then R[x]/(xn) is a reversible ring, where (xn) is the ideal generated by xn and n is a positive integer; and that for a right Ore ring R with Q its classical right quotient ring, R is reversible if and only if Q is reversible.