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Radicals of regular near-rings

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Abstract

Analogues of ring theory results concerning the Jacobson radical of a regular ring are obtained for near-rings with a two-sided zero. The quasiradical and the radical-subgroup of a regular near-ring are shown to be {0}. Some sufficient conditions are obtained for the radical and the primitiveradical of a regular near-ring to be {0}. Necessary and sufficient conditions are determined for a near-ringR which satisfies d. c. c. onR-subgroups ofR to be regular.

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  1. Department of Mathematics and Computer Science, University of South Carolina, 29208, Columbia, SC, USA

    Marjory J. Johnson

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  1. Marjory J. Johnson
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Johnson, M.J. Radicals of regular near-rings. Monatshefte für Mathematik 80, 331–341 (1975). https://doi.org/10.1007/BF01472581

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