EXTENSIONS OF STRONGLY α-REVERSIBLE RINGS

We introduce the notion of strongly α-reversible ringswhich is a strong version of α-reversible rings, and investigate itsproperties. We first give an example to show that strongly reversiblerings need not be strongly α-reversible. We next argue about thestrong α-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown that a ring Ris strongly right α-reversible if and only if its polynomial ring R[x]is strongly right α-reversible if and only if its Laurent polynomialring R[x, x^−1] is strongly right α-reversible. Moreover, we introducethe concept of Nil-α-reversible rings to investigate the nilpotentelements in α-reversible rings. Examples are given to show thatright Nil-α-reversible rings need not be right α-reversible.