Vol. 58, No. 2, 1975

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Radicals of supplementary semilattice sums of associative rings

Barry J. Gardner

Vol. 58 (1975), No. 2, 387–392

This paper deals with the effect of radicals (in the Kurosh-Amitsur sense) on supplementary semilattice sums of rings as defined by J. Weissglass (Proc. Amer. Math. Soc., 39 (1973), 471-473). It is shown that if is a strict, hereditary radical class, then (R) = ΣαΩ(Rα) for every supplementary semilattice sum R = ΣαΩRα with finite Ω. If is an A-radical ciass or the generalized nil radical class, the same conclusion holds with the finiteness restriction removed. On the other hand, if αΩRα) = ΣαΩ(Rα) for all finite Ω, then is strict and satisfies ()R ∈ℜ⇒ the zeroring on the additive group of R belongs to , a condition satisfled by both hereditary strict and A-radical classes.

Mathematical Subject Classification
Primary: 16A21
Received: 20 March 1974
Published: 1 June 1975
Barry J. Gardner