On the classification of commutative right-nilalgebras of nilindex 5 and dimension 4

Abstract

Gerstenhaber and Myung (1975) classified all commutative power-associative nilalgebras of dimension 4. In Elduque and Labra (2007), Gerstenhaber and Myung's results are generalized by giving a classification of commutative right-nilalgebras of right-nilindex 4 and dimension at most 4, without assuming power-associativity. In this article we complete this research and give a classification of commutative right-nilalgebras of right-nilindex 5 and dimension 4, without assuming power-associativity, thus completing the classification of commutative right-nilalgebras of dimension at most 4.