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An extension of the Krull-Schmidt theorem

Published online by Cambridge University Press:  17 April 2009

S. B. Conlon
S. B. Conlon
Affiliation:
Department of Mathematics (Pure Mathematics), University of Sydney, Sydney. New South Wales.
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Abstract

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In the usual Krull-Schmidt-Azumaya theorem in abelian categories it is essential that each of the direct summands has a local ring of endomorphisms. A partial answer is given here to the case where this last condition is not satisfied by the indecomposable direct summands. It is found that those summands with local endomorphism rings are determined up to isomorphism and cardinality of occurrence.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 1 , April 1969 , pp. 109 - 114
Copyright
Copyright © Australian Mathematical Society 1969

References

[1] Azumaya, Gôro, “Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt's theorem”, Nagoya Math. J., 1 (1950), 117–124.CrossRefGoogle Scholar
[2] Gabriel, Pierre, Objects injectifs dans les catégories abéliennes, (Séminaire Dubriel, M.-L. Dubreil-Jacotin et Pisot, Exposition No. 17, Faculté des Sciences de Paris, Paris, 1958/1959).Google Scholar