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Lattices of Radicals of Involution Rings

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Algebra Colloquium

Abstract

A lattice-theoretic approach to the radical theory of rings was initiated by Snider. In the current paper, we extend this approach to the radical theory of involution rings. We show that the classes of hereditary radicals, radicals satisfying ADS and invariant radicals form complete sublattices of the lattice of all radicals of involution rings. We show that certain sublattices are isomorphic to sublattices of the lattice of radicals of rings. We characterize the atoms of certain lattices of radicals of involution rings.

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Author notes

  1. G. L. Booth

    Present address: Department of Mathematics, University of Port Elizabeth, P.O. Box 1600, Port Elizabeth, 6000, South Africa

Authors and Affiliations

  1. Department of Mathematics, University of Transkei, Umtata, South Africa

    G. L. Booth

  2. Department of Mathematics, University of Port Elizabeth, Port Elizabeth, South Africa

    N. J. Groenewald

Authors
  1. G. L. Booth
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  2. N. J. Groenewald
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Additional information

Communicated by R. Wiegandt

1991 Mathematics Subject Classification: 16W10, 16N99, 06B99

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Booth, G.L., Groenewald, N.J. Lattices of Radicals of Involution Rings. Algebra Colloq. 7, 17–26 (2000). https://doi.org/10.1007/s10011-000-0017-1

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  • DOI: https://doi.org/10.1007/s10011-000-0017-1

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