LIE ISOMORPHISMS IN PRIME-RINGS WITH INVOLUTION

Let R and R' be prime rings with involutions of the first kind and with respective Lie subrings of skew elements K and K'. Furthermore assume (RC:C) not-equal 1, 4, 9, 16, 25, 64, where C is the extended centroid of R. It is shown that any Lie isomorphism of K onto K' can be extended uniquely to an associative isomorphism of [K] onto [K'], where [K] and [K'] are respectively the associative subrings generated by K and K'.