Left, right, and inner socles of associative systems

In this paper we investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals.

(This paper has appeared in Acta Math. Hungar. 103 (2004), no. 3, 177--196)

J. A. Anquela < anque@pinon.ccu.uniovi.es >

T. Cortes < cortes@pinon.ccu.uniovi.es >

M. Gomez-Lozano < magomez@agt.cie.uma.es >

M. Siles-Molina < mercedes@agt.cie.uma.es >