EXAMPLES OF COMMUTATIVE RIGHT-NILALGEBRAS OVER SMALL FIELDS

Correa et al. (2003) proved that any commutative right-nilalgebra of nilindex 4 and dimension 4 is nilpotent in characteristic =2 3. They did not assume powerassociativity. In this article we will further investigate these algebras without the assumption on the dimension and providing examples in those cases that are not covered in the classification concentrating mostly on algebras generated by one element