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Radicals whose semisimple classes satisfy a generalised ADS condition

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Abstract

A class K of rings has the GADS property (i.e., generalized ADS property) if wheneverX◃ I◃ R with X∈ K, then there exists B ◃ R with B ∈ K such that X ⊆ B ⊆ I. Radicals whose semisimple classes have the GADS property are called g-radicals. In this paper, we fully characterize the class of g -radicals. We show that ? is a g-radical if and only if either ? ⊆ I or S? ⊆ I , whereI denotes the class of idempotent rings and S? denotes the semisimple class of ?. It is also shown that the (hereditary) g-radicals form an (atomic) sublattice of the lattice of all radicals.

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Authors and Affiliations

  1. University of Louisiana at Lafayette, Lafayette, La, 70504, U.S.A

    G.F. Birkenmeier

  2. University of Port Elizabeth, Port Elizabeth, 6000, South Africa

    G.L. Booth & N.J. Groenewald

Authors
  1. G.F. Birkenmeier
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  2. G.L. Booth
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  3. N.J. Groenewald
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Birkenmeier, G., Booth, G. & Groenewald, N. Radicals whose semisimple classes satisfy a generalised ADS condition. Acta Mathematica Hungarica 102, 239–248 (2004). https://doi.org/10.1023/B:AMHU.0000023219.02623.4c

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  • DOI: https://doi.org/10.1023/B:AMHU.0000023219.02623.4c

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