UNITARY ELEMENTS IN SIMPLE ARTINIAN-RINGS

The problem of determining when a unitary element is a product of Cayl ey unitary elements is completely solved for simple artinian rings of characteristic not 2. Theorem 1. Let D be a division ring of character istic not 2. Suppose that R = D-n assumes an involution which induces a non-identity involution on D. Then any unitary element in R is a pro duct of two Cayley unitary elements. Theorem 2. Let F be a field of ch aracteristic not 2. Suppose that R = F-n assumes an involution of th e first kind. Then any unitary element in R which is a product of Cayl ey unitary elements must have determinant 1. Conversely, any unitary e lement in R of determinant 1 is a product of two Cayley unitary elemen ts, except when F GH(3), n = 2, and is given by ((alphabeta)(gammade lta)) = ((alpha-gamma)(-betadelta)). (C) 1995 Academic Press, Inc.