The radicals of moduli are investigated as functors. Particular attention is given over to the derivatives of the functor of a radical. The function R0r turns out to be a hereditary radical containing the given one. Several relations between the Rir are proved. The article is concluded with a description of the hereditary radicals of a Prüfer ring. All the radicals of a Prüfer ring have the form of torsions in an integral domain.
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A. Cartan and S. Eilenberg, Homological Algebra, Princeton U. Press (1956).
C. E. Watts, “Intrinsic characterizations of some additive functors,” Proc. Am. Math. Soc.,11, No. 1, 5–8 (1960).
Translated from Matematicheskie Zametki, Vol. 3, No. 6, pp. 633–642, June, 1968.
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Govorov, V.E. Derivatives of the radicals of moduli. Mathematical Notes of the Academy of Sciences of the USSR 3, 403–409 (1968). https://doi.org/10.1007/BF01110596
- Integral Domain
- Hereditary Radical