Lie Isomorphisms in Prime Rings with Involution Original Research Article

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) ≠ 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 left angle bracketKright-pointing angle bracket onto left angle bracketK′right-pointing angle bracket, where left angle bracketKright-pointing angle bracket and left angle bracketK′right-pointing angle bracket are respectively the associative subrings generated by K and K′.