Let 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, (Formula presented.). Condition 2: For each x in R, there is an integer N = N(x)≥1 depending on x such that (Formula presented.) where dx is the map of R defined by dx(y): = yx−xy, for all y in R, and (Formula presented.) is the Nth power of dx (under composition). Condition 3: For each x in R, there is an integer (Formula presented.) depending on x such that (Formula presented.).

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Keywords Algebraic over the center, commuting involution, integral over the center, local Engel condition, local power commuting condition
Persistent URL dx.doi.org/10.1080/00927872.2016.1237641
Journal Communications in Algebra
Citation
Chacron, M. (2017). More on involutions with local Engel or power commuting conditions. Communications in Algebra, 45(8), 3503–3514. doi:10.1080/00927872.2016.1237641