Nondegenerate Jordan Algebras Satisfying Local Goldie Conditions
✍ Scribed by Antonio Fernández López; Eulalia Garcı́a Rus
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 126 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
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 the main results of a Ž Ž . . previous paper by the authors J. Algebra 174 1995 , 1024᎐1048 , it is obtained that such Jordan algebras J are precisely the local orders in nondegenerate Jordan algebras satisfying dcc on principal inner ideals and without non-artinian quadratic ideals, which extends to local orders the Zel'manov theorem for Goldie Jordan algebras.