Abstract
ABSTRACTLet R be a ring with * and with 1. Assume that R has no nil ideals (other than 0) and that R is integral over its center Z, that is to say, that each x in R satisfies a monic polynomial equation (in x) with coefficients in Z. Then the following conditions are equivalent. Condition 1: * is a commuting (or normal) involution, that is, for each x in R, . Condition 2: For each x in R, there is an integer N = N(x)≥1 depending on x such that where dx is the map of R defined by dx(y): = yx−xy, for all y in R, and is the Nth power of dx (under composition). Condition 3: For each x in R, there is an integer depending on x such that .
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