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 is an element of J. AS a consequence of this theorem and of the main results of a 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 dec on principal inner ideals and without non-artinian quadratic ideals, which extends to local orders the Zel'manov theorem for Goldie Jordan algebras. (C) 1996 Academic Press, Inc. [References: 10]
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