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On \(n\)th order plenary idempotents in a Gonshor genetic algebra. (English) Zbl 0608.17014
The plenary powers of an element x in nonassociative algebra are defined as follows \[ x^{[1]}=x,\quad x^{[n+1]}=x^{[n]}x^{[n]}. \] The authors define an element \(x\) to be a plenary idempotent of order \(n\) if \(x^{[n]}=x\). The main result of the paper gives a sufficient condition for the existence of an \(r\)-parameter family of plenary idempotents of order \(r\). The condition is quite technical.
MSC:
17D92 Genetic algebras
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