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Isomorphisms between endomorphism rings of projective modules

Published online by Cambridge University Press:  18 May 2009

José Luis García  and
Juan Jacobo Simón
José Luis García
Affiliation:
Department of MathematicsUniversity of Murcia30071 Murcia, Spain
Juan Jacobo Simón
Affiliation:
Department of MathematicsUniversity of Murcia30071 Murcia, Spain
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Let R and S be arbitrary rings, RM and SN countably generated free modules, and let φ:End(RM)→End(sN) be an isomorphism between the endomorphism rings of M and N. Camillo [3] showed in 1984 that these assumptions imply that R and S are Morita equivalent rings. Indeed, as Bolla pointed out in [2], in this case the isomorphism φ must be induced by some Morita equivalence between R and S. The same holds true if one assumes that RM and SN are, more generally, non-finitely generated free modules.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 353 - 355
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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