Summary
We study Hestenes rings (H-rings)R and we give a characterization of the Jacobson radicalJ(R). We prove that ifR is semisimple thenR is a subdirect sum of quasi-primitive H-rings, and that ifR has D.C.C. on right ideals thenJ(R) is nilpotent and every nil right ideals ofR lies inJ(R). Moreover we show that ifR is a H-ring with A.C.C. on right (left) ideals, then every nil right ideal is nilpotent and avery nil left ideal is nilpotent.
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Lavoro eseguito in qualità di borsista del C.N.R. nell'ambito del “Gruppo nazionale per le strutture algebriche e geometriche e loro applicazioni”.
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Spera, A.G. Sugli anelli ternari di Hestenes. Rend. Circ. Mat. Palermo 27, 289–304 (1978). https://doi.org/10.1007/BF02843940
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DOI: https://doi.org/10.1007/BF02843940