# zbMATH — the first resource for mathematics

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
##### Keywords:
genetic algebra; plenary powers; plenary idempotent