Abstract
A celebrated theorem for Jordan algebras due to Zel’manov [19, 20] states that a (linear) Jordan algebra J is an order in a semisimple artinian Jordan algebra Q if and only if J is semiprime, satisfies the annihilator chain condition, and does not contain infinite direct sums of inner ideals. Reciently [10], a notion of local order has been introduced in a (not necessarily unital) associative ring and proved a Goldie-like characterization of local orders in semiprime rings with dcc on principal one-sided ideals [11], equivalently, coinciding with their socles. Inspired by these ideas, we developed in [5, 6] a theory of local orders in Jordan algebras which need not have a unit and proved a natural extension of Zel’manov-Goldie theorem.
In this note we provide a quick approach to this result, giving the relevant definitions and the main tools used in its proof.
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© 1994 Springer Science+Business Media Dordrecht
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López, A.F., Rus, E.G. (1994). An Extension of the Zel’Manov-Goldie Theorem. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_22
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DOI: https://doi.org/10.1007/978-94-011-0990-1_22
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