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An algebraic dependence over the quasi-centre

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Summary

The authors study a class of rings generalizing both ξ-rings and rings which are (1) quasi-radical over their normalizer. The results are quite complete in the Noetherian case. In application several conditions on rings are shown to force the right duo condition. In particular it is shown that ξ-rings, algebras over the rationals satisfying (1), and algebraic algebras having no non central nilpotent elements (or a more general condition) are right duo or duo rings.

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Entrata in Redazione il 28 luglio 1972.

This research has been supported by grant A7876 of the National Research Council of Canada.

This research has been supported by grant A7877 of the National Research Council of Canada.

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Chacron, M., Thierrin, G. An algebraic dependence over the quasi-centre. Annali di Matematica 110, 1–14 (1976). https://doi.org/10.1007/BF02418000

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Keywords

  • General Condition
  • Nilpotent Element
  • Algebraic Dependence
  • Algebraic Algebra
  • Noetherian Case