Abstract
Recently Britten has proven an analog of Goldieâs theorem for the Jordan ring $S$ of symmetric elements in a ring with involution of characteristic not 2. In this paper we first extend Brittenâs theorem to the situation where $R$ is an arbitrary ring and the Jordan ring is only an ample subring of the symmetric elements. We apply this result to show that if $S$ has ACC on quadratic ideals, then the (Jordan) nil radical of $S$ is nilpotent.
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