We consider the determination of ring radicals by classes of modules as first discussed by Andrunakievich and Ryabukhin, but
in cases where the modules concerned are defined by additive properties. Such a radical is the upper radical defined by the
class of subrings of a class of endomorphism rings of abelian groups and is therefore strict. Not every strict radical is
of this type, and while the A-radicals are of this type, there are others, including some special radicals. These investigations bring radical theory into
contact with (at least) two questions from other parts of algebra. Which rings are endomorphism rings? For a given ring R, which abelian groups are non-trivial R-modules?
Connections between radicals of alternative and right alternative rings are investigated, with emphasis on those which are
nondegenerate in the sense that semi-simple rings have no absolute zero-divisors. In particular it is shown that nondegenerate
radicals of right alternative rings have the Anderson-Divinsky-Sulinski property.
Authors:A. Dvaranauskait?, P. R. Venskutonis, and J. Labokas
Bandonienė, D., Murkovic, M., Pfannhauser, W., Venskutonis, P.R. & Gruzdienė, D. (2002): Detection and activity evaluation of radical scavenging compounds by using DPPH free radical and on-line HPLC-DPPH methods. Eur. Fd Res. Technol. , 214, 143