RIGHT ALTERNATIVE RINGS WITH x(yz)−y(xz) IN THE CENTER

Abstract

In [1] it was proved that if R is a prime right alternative ring of char.  ≠ 2, 3 with (R, R, U ) ⊆ U or S(x², x, y) = 0, then either U = C or R is strongly (−1, 1).  In this paper first we prove that if R is a prime right alternative ring with x(yz) - y(xz) ∈ U, then (R, R, U ) ⊆ U.  Using this we prove that either U = C or R is strongly (−1, 1).