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Abstract  

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?

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Kurosh–Amitsur prime radical for near-rings Comm. in Algebra 18 3111 – 3122 10.1080/00927879008824063 . [5] Groenewald , N. J. 1988 Strongly prime near

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Abstract  

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.

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Lu, C. P. , M-Radicals of submodules in modules, II, Math. Japonica , 35 (1990), no. 5, 991–1001. MR 92b :13014 Lu C. P. M-Radicals

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Acta Mathematica Hungarica
Authors: Daniel Ceretto, Esther García, and Miguel Gómez Lozano

References [1] Beattie , M. Stewart , P. 1991 Graded radicals of graded rings Acta Math. Hungar

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Acta Alimentaria
Authors: Rajeev Bhat, K. Sridhar, B. Bhushan, and A. Sharma

160 Szöcs, F. (2002): Walnut free radicals studied by ESR. J. Fd Sci. , 67 , 953–955. Szöcs F

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Orvosi Hetilap
Authors: Mihály Murányi, Ali Salah Morshed, Mátyás Benyó, Csaba Tóth, and Tibor Flaskó

.: Increasing incidence of minimal residual cancer in radical prostatectomy specimens. Am. J. Surg. Pathol., 1997, 21 , 174–178. Epstein J. I. Increasing incidence of minimal residual cancer

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Nagy, I. Z.: Semiconduction of proteins as an attribute of the living state: the ideas of Albert Szent-Györgyi revisited in light of the recent knowledge regarding oxygen free radicals. Exp

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in Noncommutative Rings , Graduate Texts in Mathematics , 131 , Springer-Verlag , New York , ( 1991 ). [5] L axton , R. R. , A radical and its theory for

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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

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