Abstract
Gerstenhaber and Myung (Citation1975) classified all commutative, power-associative nilalgebras of dimension 4. In this article we extend Gerstenhaber and Myung's results by giving a classification of commutative right-nilalgebras of right-nilindex four and dimension at most four, without assuming power-associativity. For quadratically closed fields there is, up to isomorphism, a unique such algebra which is not power-associative in dimension 3, and 7 in dimension 4.
A.M.S. (2000) Subject Classification:
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 University of Chile on grants from FONDECYT 7030075 and 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 M. Ferrero.