Abstract
A preradical is a normal subfunctor of the identity-functor. In this note I give a correspondence between preradicals and classes of morphisms in rather general categories. For a classI of morphisms R I , defined by R I C=∩Ke (if|iεI and fεMor (C, Range (i)) is a preradical and-all preradicals are of this type. As an interesting application I give a characterisation of the set of all left exact preradicals for A-modules. Also I have obtained results about quasi-injective A-modules for a Noetherian ring A. Ich danke Herrn Prof. Dr. Kasch für seine Anregungen, den Gutachtern für ihre Hinweise.
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Literatur
N. Bourbaki “Algèbre comm.” chap.2 Paris Hermann 1961
B. Charles “Studies on abelian groups” Berlin-Heidelberg-New York Springer und Paris Dunod 1968
N. J. Divinsky “Rings and Radicals” 1.Aufl. London Allen & Unwin 1965
S.Eilenberg, J.C.Moore “Foundation of Relative Homological Algebra” Mem. Amer.math.Soc. 55 (1966)
P.Freyd “Representation in Abelian categories” Conf.of Cat. La Yolla 95–120 (1965)
P. Gabriel “Catégories Abéliennes” Bull.Soc.math.France 90 323–448 (1962)
Johnson R.E., Wong E.T. “Quasiinjective modules and irreducible rings” Journal London math.Soc. 36 260–268 (1961)
J. Maranda “Injective Structures” Trans.Amer.math.Soc. 110 98–135 (1964)
L.E.T. Wu und J. P. Jans, “On quasi-projectives” Illinois J.Math. 11 439–448 (1967)
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Hauger, G. Präradikale und Morphismenklassen. Manuscripta Math 2, 397–402 (1970). https://doi.org/10.1007/BF01719594
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DOI: https://doi.org/10.1007/BF01719594