Chain conditions on symmetric elements

Montgomery, Susan

doi:10.1090/S0002-9939-1974-0349736-6

Chain conditions on symmetric elements
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by Susan Montgomery PDF

Proc. Amer. Math. Soc. 46 (1974), 325-331 Request permission

Abstract:

Recently Britten has proven an analog of Goldie’s theorem for the Jordan ring $S$ of symmetric elements in a ring with involution of characteristic not 2. In this paper we first extend Britten’s 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.

References

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