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Acta Mathematica Hungarica
Authors:
Daniel Ceretto
,
Esther García
, and
Miguel Gómez Lozano

Abstract

For an arbitrary group G and a G-graded Lie algebra L over a field of characteristic zero we show that the Kostrikin radical of L is graded and coincides with the graded Kostrikin radical of L. As an important tool for our proof we show that the graded Kostrikin radical is the intersection of all graded-strongly prime ideals of L. In particular, graded-nondegenerate Lie algebras are subdirect products of graded-strongly prime Lie algebras.

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Acta Mathematica Hungarica
Authors:
José Anquela
,
Teresa Cortés
,
Miguel Gómez-Lozano
, and
Mercedes Siles-Molina

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.

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