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Categories whose objects are determined by their rings of endomorphisms

Published online by Cambridge University Press:  17 April 2009

Grigore Călugăreanu jr
Grigore Călugăreanu jr
Affiliation:
Department of Mathematics, Universitatea “Babes-Bolyai”, Cluj-Napoca, Roumania.
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Abstract

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In an additive category A0, objects are said to be determined by their rings of endomorphisms if for each ring-isomorphism F of the rings of endomorphisms of two objects A, B in A0 there is an isomorphism f: A → B in A0 such that F(α) = fαf-1, for every endomorphism α of A. Considering.this problem in the context of closed categories (in Eilenberg and Kelly's sense), the author proves a general theorem which generalises results of Eidelheit (for real Banach spaces) and of Kasahara (for real locally convex spaces).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 65 - 72
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Eidelheit, M., “On isomorphisms of rings of linear operators”, Studia Math. 9 (1940), 97–105.CrossRefGoogle Scholar
[2]Eilenberg, Samuel and Kelly, G. Max, “Closed categories”, Proceedings of the Conference on Categorical Algebra, La Jolla, 1965, 421–562 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).Google Scholar
[3]Kasahara, Shouro, “Sur l'espace des endomorphismes continus de l'espace vectoriel localement convexe”, Math. Japon. 3 (1955), 111–116.Google Scholar
[4]Mitchell, Barry, Theory of categories (Pure and Applied Mathematics, 17. Academic Press, New York and London, 1965).Google Scholar