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Herstein's Theorems and Simplicity of Hermitian Jordan Systems

✍ Scribed by José A Anquela; Teresa Cortés; Esther Garcı́a

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
186 KB
Volume
246
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to professor j. marshall osborn on the occasion of his retirement

In this paper we extend Herstein's first construction relating associative and Jordan ideals to pairs and triple systems. As a consequence we show that an associative pair or triple system is simple if and only if its Jordan symmetrization is simple. We also generalize Herstein's second construction to ample subsystems of associative algebras, pairs, and triple systems, which provides information on their simplicity when the associative structure is simple.

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In this paper we prove that the local algebras of a simple Jordan pair are simple. Jordan pairs all of which local algebras are simple are also studied, showing that they have a nonzero simple heart, which is described in terms of powers of the original pair. Similar results are given for Jordan tri

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