LIE ISOMORPHISMS IN PRIME-RINGS WITH INVOLUTION

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