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.

Key Words:

• Nilpotency
• Power-associative
• Right-nilalgebras

2000 Mathematics Subject Classification:

• 17A30

ACKNOWLEDGMENTS

The authors thank the referee for suggestions and comments for improvement of the article.

Part of this research was done while the first author was visiting Universidad de Chile on a grant from FONDECYT 7050164. Support is also acknowledged from the Spanish Ministerio de Educación y Ciencia and FEDER (MTM 2004-08115-C04-02) and from the Diputación General de Aragón (Grupo de Investigación de Álgebra)

The second author was supported by FONDECYT 1030919.

Notes

Communicated by I. P. Shestakov.