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Radicals of Jordan rings connected with alternative rings

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Abstract

Subject to a certain restriction on the additive group of an alternative ring A, we prove that R(A)=R(A(+)), where A(+) is a Jordan ring and R is one of the following radicals: the Jacobson radical, the upper nil-radical, the locally nilpotent radical, or the lower nil-radical. For the proof of these relationships Herstein's well-known construction for associative rings is generalized to alternative rings.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, USSR

    A. M. Slin'ko

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  1. A. M. Slin'ko
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Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 135–140, July, 1974.

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Slin'ko, A.M. Radicals of Jordan rings connected with alternative rings. Mathematical Notes of the Academy of Sciences of the USSR 16, 664–667 (1974). https://doi.org/10.1007/BF01098823

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  • DOI: https://doi.org/10.1007/BF01098823

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