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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1974, Volume 16, Issue 6, Pages 933–942 (Mi mz7535)

Annihilator conditions in endomorphism rings of modules

G. M. Brodskii

Yaroslavl State University

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 $r(l(I))=I$ and $l(r(J))=J$ for all finitely generated right ideals $I$ and finitely generated left ideals $J$.

Full text: PDF file (748 kB)

English version:
Mathematical Notes, 1974, 16:6, 1153–1158

Bibliographic databases:

UDC: 519.4

Citation: G. M. Brodskii, “Annihilator conditions in endomorphism rings of modules”, Mat. Zametki, 16:6 (1974), 933–942; Math. Notes, 16:6 (1974), 1153–1158

Citation in format AMSBIB
\Bibitem{Bro74} \by G.~M.~Brodskii \paper Annihilator conditions in endomorphism rings of modules \jour Mat. Zametki \yr 1974 \vol 16 \issue 6 \pages 933--942 \mathnet{http://mi.mathnet.ru/mz7535} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=382336} \zmath{https://zbmath.org/?q=an:0308.16017} \transl \jour Math. Notes \yr 1974 \vol 16 \issue 6 \pages 1153--1158 \crossref{https://doi.org/10.1007/BF01098442}