On the nilpotence of the multiplication operator in commutative right nil algebras

Correa, I.; Hentzel, IR; Labra, A

Abstract

We study conditions under which the identity ((xx)x)x = 0 in a commutative nonassociative algebra A implies Rx is nil-potent where Rx is the multiplication operator Rx(y) = xy for all y in A. The separate conditions that we found to be sufficient are (1) dimension four or less, (2) any additional non-trivial identity of degree four, or (3) ((xx)x)(xx) = 0. We assume characteristic ? 2, 3.

Más información

Título según WOS: On the nilpotence of the multiplication operator in commutative right nil algebras
Título según SCOPUS: On the nilpotence of the multiplication operator in commutative right nil algebras
Título de la Revista: COMMUNICATIONS IN ALGEBRA
Volumen: 30
Número: 7
Editorial: TAYLOR & FRANCIS INC
Fecha de publicación: 2002
Página de inicio: 3473
Página final: 3488
Idioma: English
URL: http://www.tandfonline.com/doi/abs/10.1081/AGB-120004499
DOI:

10.1081/AGB-120004499

Notas: ISI, SCOPUS