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Goldie Theory for Jordan Algebras

✍ Scribed by Antonio Fernández López; Eulalia Garcı́a Rus; Fernando Montaner

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
498 KB
Volume
248
Category
Article
ISSN
0021-8693

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✦ Synopsis

dedicated to professor holger petersson on the occasion of his 60th birthday

It is shown that Zelmanov's version of Goldie's conditions still characterizes quadratic Jordan algebras having an artinian algebra of quotients which is nondegenerate. At the same time, Jordan versions of the main notions of the associative theory, such as those of the uniform ideal, uniform element, singular ideal, and uniform dimension, are studied. Moreover, it is proved that the nondegenerate unital Jordan algebras of finite capacity are precisely the algebras of quotients of nondegenerate Jordan algebras having the property that an inner ideal is essential if and only if it contains an injective element.  2002 Elsevier Science (USA)

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Nondegenerate Jordan Algebras Satisfying
Nondegenerate Jordan Algebras Satisfying Local Goldie Conditions
✍ Antonio Fernández López; Eulalia Garcı́a Rus 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 126 KB

A structure theorem is given for nondegenerate Jordan algebras J satisfying the ascending chain condition on annihilators of a single element and such that J contains no infinite direct sum of inner deals inside the inner ideal generated by each element x g J. As a consequence of this theorem and of