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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 2(6), Pages 226–242 (Mi msb3679)  

This article is cited in 2 scientific papers (total in 2 papers)

Endomorphism rings of free modules

G. M. Brodskii


Abstract: Suppose $\mathfrak a$ is some property of modules. Let $\mathfrak{R_a}$ denote the class of rings over which all modules possess property $\mathfrak a$. The main theorem of this paper answers the following question for a rather extensive class of properties $\mathfrak a$; what must the property $\mathfrak b$ of modules be in order that $R\in\mathfrak{R_a}$ if and only if $\operatorname{End}_R(F)\in\mathfrak{R_b}$, for any free $R$-module $F$? Among the corollaries are many well-known theorems relating properties of the ring $R$ and the rings $\operatorname{End}_R(F)$, and also a number of new results of similar type.
Bibliography: 35 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:2, 215–231

Bibliographic databases:

UDC: 519.48
MSC: 16A34, 16A36, 16A42, 16A50, 16A52, 18E40, 18G05
Received: 20.08.1973

Citation: G. M. Brodskii, “Endomorphism rings of free modules”, Mat. Sb. (N.S.), 94(136):2(6) (1974), 226–242; Math. USSR-Sb., 23:2 (1974), 215–231

Citation in format AMSBIB
\Bibitem{Bro74}
\by G.~M.~Brodskii
\paper Endomorphism rings of free modules
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 2(6)
\pages 226--242
\mathnet{http://mi.mathnet.ru/msb3679}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=349761}
\zmath{https://zbmath.org/?q=an:0306.16011}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 2
\pages 215--231
\crossref{https://doi.org/10.1070/SM1974v023n02ABEH002177}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Barbara L. Osofsky, “Weak global dimension of endomorphism rings of free modules”, Journal of Pure and Applied Algebra, 24:2 (1982), 203  crossref  mathscinet  zmath
    2. Juan Jacobo Simón, “Finitely Generated Projective Modules over Row and Column Finite Matrix Rings”, Journal of Algebra, 208:1 (1998), 165  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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