Left, right, and inner socles of associative systems |
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| Authors: | José A. Anquela Teresa Cortés Miguel Gómez-Lozano Mercedes Siles-Molina |
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| Affiliation: | (1) Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo S/N, 33007 Oviedo, Spain;(2) Departamento de álgebra, Geometría, y Topología, Facultad de Ciencias, Universidad de Málaga, Campus De Teatinos, 29071 Málaga, Spain |
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| Abstract: | 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 revised version was published online in June 2006 with corrections to the Cover Date. |
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| Keywords: | and pair socle left triple system right associative algebra and inner ideal |
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