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Fundam. Prikl. Mat., 2008, Volume 14, Issue 2, Pages 207–221 (Mi fpm1120)  

This article is cited in 4 scientific papers (total in 4 papers)

Rings without infinite sets of noncentral orthogonal idempotents

A. A. Tuganbaev

Russian State University of Trade and Economics

Abstract: Let $A$ be a ring without infinite sets of noncentral orthogonal idempotents. $A$ is an exchange ring if and only if all Pierce stalks of $A$ are semiperfect rings. All $A$-modules are $I_0$-modules if and only if either $A$ is a right semi-Artinian ring in which every proper right ideal is the intersection of maximal right ideals or $A/\operatorname{SI}(A_A)$ is an Artinian serial ring such that the square of the Jacobson radical of $A/\operatorname{SI}(A_A)$ is equal to zero.

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English version:
Journal of Mathematical Sciences (New York), 2009, 162:5, 730–739

Bibliographic databases:

UDC: 512.55

Citation: A. A. Tuganbaev, “Rings without infinite sets of noncentral orthogonal idempotents”, Fundam. Prikl. Mat., 14:2 (2008), 207–221; J. Math. Sci., 162:5 (2009), 730–739

Citation in format AMSBIB
\Bibitem{Tug08}
\by A.~A.~Tuganbaev
\paper Rings without infinite sets of noncentral orthogonal idempotents
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 2
\pages 207--221
\mathnet{http://mi.mathnet.ru/fpm1120}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2475601}
\zmath{https://zbmath.org/?q=an:05660184}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 162
\issue 5
\pages 730--739
\crossref{https://doi.org/10.1007/s10958-009-9656-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350650471}


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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. A. N. Abyzov, A. A. Tuganbaev, “Rings over which all modules are $I_0$-modules. II”, J. Math. Sci., 162:5 (2009), 587–593  mathnet  crossref  mathscinet  zmath
    2. A. N. Abyzov, A. A. Tuganbaev, “Submodules and direct summands”, J. Math. Sci., 164:1 (2010), 1–20  mathnet  crossref  mathscinet
    3. A. N. Abyzov, “Generalized $SV$-rings of bounded index of nilpotency”, Russian Math. (Iz. VUZ), 55:12 (2011), 1–10  mathnet  crossref  mathscinet
    4. A. N. Abyzov, “$I_0^*$-modules”, Russian Math. (Iz. VUZ), 58:8 (2014), 1–14  mathnet  crossref
  • Фундаментальная и прикладная математика
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