Lattices of Radicals of Involution Rings |
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| Authors: | G. L. Booth N. J. Groenewald |
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| Affiliation: | (1) Department of Mathematics, University of Transkei, Umtata, South Africa;(2) Department of Mathematics, University of Port Elizabeth, Port Elizabeth, South Africa;(3) Present address: Department of Mathematics, University of Port Elizabeth, P.O. Box 1600, Port Elizabeth, 6000, South Africa |
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| 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.1991 Mathematics Subject Classification: 16W10, 16N99, 06B99 |
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| Keywords: | involution ring radical symmetric radical invariant radical lattice of radicals |
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