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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 4(12), Pages 518–529 (Mi msb3425)  

More on quasi-Frobenius rings

L. A. Skornyakov


Abstract: Let $R$ be a ring and $J$ its Jacobson radical. Let us set $J^1=J$, $J^\alpha=JJ^{\alpha-1}$, and $J^\alpha=\bigcap_{\beta<\alpha}J^\beta$ if $\alpha$ is a limit ordinal. We call a ring an annihilating ring if the left (right) annihilator of the right (left) annihilator of an arbitrary left (right) ideal $I$ is $I$ itself. We prove that a ring $R$ is quasi-Frobenius if and only if it is a left self-injective annihilating ring and $J^\alpha=0$ for some transfinite $\alpha$.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:4, 511–522

Bibliographic databases:

UDC: 519.48
MSC: 16A36, 16A34, 16A52
Received: 07.06.1973

Citation: L. A. Skornyakov, “More on quasi-Frobenius rings”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 518–529; Math. USSR-Sb., 21:4 (1973), 511–522

Citation in format AMSBIB
\Bibitem{Sko73}
\by L.~A.~Skornyakov
\paper More on quasi-Frobenius rings
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 4(12)
\pages 518--529
\mathnet{http://mi.mathnet.ru/msb3425}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=332869}
\zmath{https://zbmath.org/?q=an:0282.16013}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 4
\pages 511--522
\crossref{https://doi.org/10.1070/SM1973v021n04ABEH002032}


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