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Mat. Sb., 2003, Volume 194, Number 12, Pages 93–122 (Mi msb788)  

This article is cited in 9 scientific papers (total in 9 papers)

Multiplication modules over non-commutative rings

A. A. Tuganbaev

Moscow Power Engineering Institute (Technical University)

Abstract: It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If $A$ is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated $A$-module $M$ is a multiplicative module if and only if all its localizations with respect to maximal right ideals of $A$ are cyclic modules over the corresponding localizations of $A$. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings.

DOI: https://doi.org/10.4213/sm788

Full text: PDF file (401 kB)
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English version:
Sbornik: Mathematics, 2003, 194:12, 1837–1864

Bibliographic databases:

UDC: 512.55
MSC: 16Dxx
Received: 13.08.2002

Citation: A. A. Tuganbaev, “Multiplication modules over non-commutative rings”, Mat. Sb., 194:12 (2003), 93–122; Sb. Math., 194:12 (2003), 1837–1864

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Medina-Barcenas M., Morales-Callejas L., Shaid Sandoval-Miranda M.L., Zaldivar-Corichi A., “On Strongly Harmonic and Gelfand Modules”, Commun. Algebr.  crossref  mathscinet  isi
    2. Zhang Guoyin, Tong Wenting, Wang Fanggui, “Spectrum of a noncommutative ring”, Comm. Algebra, 34:8 (2006), 2795–2810  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Jawad Abuhlail, “A Zariski Topology for Modules”, Communications in Algebra, 39:11 (2011), 4163  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Jawad Abuhlail, “A dual Zariski topology for modules”, Topology and its Applications, 158:3 (2011), 457  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Jawad Abuhlail, “Zariski Topologies for Coprime and Second Submodules”, Algebra Colloq, 22:01 (2015), 47  crossref  mathscinet  zmath  scopus  scopus
    6. Wijayanti I.E., “on Left Residuals of Submodules in Fully Multiplication Modules”, JP J. Algebr. Number Theory Appl., 36:1 (2015), 17–28  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. Groenewald N.J., Ssevviiri D., “Classical Completely Prime Submodules”, Hacet. J. Math. Stat., 45:3 (2016), 717–729  crossref  mathscinet  zmath  isi  scopus
    8. Castro Perez J., Medina Barcenas M., Rios Montes J., Zaldivar Corichi A., “On Semiprime Goldie Modules”, Commun. Algebr., 44:11 (2016), 4749–4768  crossref  mathscinet  zmath  isi  scopus
    9. Beiranvand P.K., Beyranvand R., “Almost Prime and Weakly Prime Submodules”, J. Algebra. Appl., 18:7 (2019), 1950129  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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