Título inglés |
A non-semiprime associative algebra with zero weak radical. |
Título español |
Algebra asociativa no semiprima con radical débil cero. |
Autor/es |
Haily, Abdelfattah |
Organización |
Dep. Math. Fac. Sci., El Jadida, Marruecos |
Revista |
0213-8743 |
Publicación |
1997, 12 (1): 53-60, 8 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
The weak radical, W-Rad(A) of a non-associative algebra A, has been introduced by A. Rodríguez Palacios in [3] in order to generalize the Johnson's uniqueness of norm theorem to general complete normed non-associative algebras (see also [2] for another application of this notion). In [4], he showed that if A is a semiprime non-associative algebra with DCC on ideals, then W-Rad(A) = 0. In the first part of this paper we give an example of a non-semiprime associative algebra A with DCC on ideals and W-Rad(A) = 0. As a consequence we shall see that, in the class of all associative algebras, the subclass S = {A : W-Rad(A) = 0} is not a semisimple class relative to a radical in the sense of Amitsur-Kurosh. In the second part of this paper, we shall establish the coincidence between the weak radical and the maximal nilpotent ideal in a finite dimensional Jordan algebra. |
Clasificación UNESCO |
120112 |
Palabras clave español |
Algebras asociativas ; Algebras de Jordan ; Anillos ; Espacios normados ; Grupo nilpotente |
Código MathReviews |
MR1482414 |
Código Z-Math |
Zbl 0883.16014 |
Acceso al artículo completo |