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Annihilator conditions in endomorphism rings of modules

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Abstract

The concepts of an intrinsically projective module and an intrinsically injective module are introduced and their connection with the presence of annihilator conditions in the endomorphism ring of a module is explained. It is shown that a ring R is quasi-Frobenius if and only if in the endomorphism ring of any fully projective (or any fully injective) R-module it is true that r(l(I))=I andl(r(J))=J for all finitely generated right ideals I and finitely generated left ideals J.

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Authors and Affiliations

  1. Yaranlavi State University, USSR

    G. M. Brodskii

Authors
  1. G. M. Brodskii
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Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 6, pp. 933–942, December, 1974.

The author is indebted to L. A. Skornyakov for discussions pertaining to this paper.

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Brodskii, G.M. Annihilator conditions in endomorphism rings of modules. Mathematical Notes of the Academy of Sciences of the USSR 16, 1153–1158 (1974). https://doi.org/10.1007/BF01098442

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  • DOI: https://doi.org/10.1007/BF01098442

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