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Abstract

In the past I have been concerned with the possibility of an extension of the primary decomposition of torsion abelian groups to some standing in arbitrary abelian categories satisfying at least the A.B.5 axiom of Grothendieck [7] and having complete subobject- and factor object lattices which are sets. Such a primary decomposition theorem has been proved in such a general setting only under separate hypotheses and conditions.

Received August 30, 1965.

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References

  1. Amitsur, S. A.: General theory of radicals II: Radicals in rings and bicategories. Amer. J. Math. 76, 100–125 (1954).

    Article  MathSciNet  MATH  Google Scholar 

  2. Anderson, T., N. Divinski, and A. Sulinski: Lower radical properties for associative and alternative rings (to appear).

    Google Scholar 

  3. Cartan, H., and S. Eilenberg: Homological algebra. Princeton: Princeton University Press 1956.

    MATH  Google Scholar 

  4. Dickson, S.: A torsion theory for abelian categories (to appear: Trans. Amer. Math. Soc.).

    Google Scholar 

  5. — Decomposition of modules I: Classical rings (to appear: Math. Z.).

    Google Scholar 

  6. — Decomposition of modules II: Rings without chain conditions (submitted forpublication).

    Google Scholar 

  7. Grothendieck, A.: Sur quelques points d’algèbre homologique. TÔhoku Math. J. (2) 9, 119–221 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  8. Hattori, A.: A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17, 147–158 (1960).

    MathSciNet  MATH  Google Scholar 

  9. Jans, J. P.: Some aspects of torsion (to appear).

    Google Scholar 

  10. Kurosch, A. G.: Radicals in rings and algebras. Mat. Sb. (N.S.) 33, 13–26 (1953) (Russian).

    Google Scholar 

  11. Levy, L.: Torsion-free and divisible modules over Noetherian integral domains. Can. J. Math. 15, 132–151 (1963).

    Article  MATH  Google Scholar 

  12. Maranda, J.-M.: Injective structures. Trans. Amer. Math. Soc. 110, 88–135 (1964).

    Article  MathSciNet  Google Scholar 

  13. MacLane, S.: Homology. Berlin-Göttingen-Heidelberg: Springer 1963.

    MATH  Google Scholar 

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© 1966 Springer-Verlag Berlin · Heidelberg

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Dickson, S. (1966). Direct Decompositions of Radicals. In: Eilenberg, S., Harrison, D.K., MacLane, S., Röhrl, H. (eds) Proceedings of the Conference on Categorical Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-99902-4_19

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  • DOI: https://doi.org/10.1007/978-3-642-99902-4_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-99904-8

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