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Sbornik: Mathematics, 2003, Volume 194, Issue 12, Pages 1837–1864
DOI: https://doi.org/10.1070/SM2003v194n12ABEH000788
(Mi sm788)
 

This article is cited in 15 scientific papers (total in 15 papers)

Multiplication modules over non-commutative rings

A. A. Tuganbaev

Moscow Power Engineering Institute (Technical University)
References:
Abstract: It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If AA is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated AA-module MM is a multiplicative module if and only if all its localizations with respect to maximal right ideals of AA are cyclic modules over the corresponding localizations of AA. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings.
Received: 13.08.2002
Bibliographic databases:
UDC: 512.55
MSC: 16Dxx
Language: English
Original paper language: Russian
Citation: A. A. Tuganbaev, “Multiplication modules over non-commutative rings”, Sb. Math., 194:12 (2003), 1837–1864
Citation in format AMSBIB
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\paper Multiplication modules over non-commutative rings
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\yr 2003
\vol 194
\issue 12
\pages 1837--1864
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Linking options:
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  • https://doi.org/10.1070/SM2003v194n12ABEH000788
  • https://www.mathnet.ru/eng/sm/v194/i12/p93
  • This publication is cited in the following 15 articles:
    1. Song-chol HAN, Won-jin HAN, Won-sok PAE, “Properties of the subtractive prime spectrum of a semimodule”, Hacettepe Journal of Mathematics and Statistics, 52:3 (2023), 546  crossref
    2. Le Van THUYET, Truong Cong QUYNH, “On Automorphism-invariant multiplication modules over a noncommutative ring”, IEJA, 2023, 1  crossref
    3. Han S.-Ch., Pae W.-S., Ho J.-N., “Topological Properties of the Prime Spectrum of a Semimodule”, J. Algebra, 566 (2021), 205–221  crossref  mathscinet  isi  scopus
    4. Groenewald N.J., “On Weakly Prime and Weakly 2-Absorbing Modules Over Non-Commutative Rings”, Kyungpook Math. J., 61:1 (2021), 33–48  crossref  mathscinet  isi
    5. Alsuraiheed T., Bavula V.V., “Criteria For a Direct Sum of Modules to Be a Multiplication Module Over Noncommutative Rings”, J. Algebra, 584 (2021), 69–88  crossref  mathscinet  isi
    6. Medina-Barcenas M., Morales-Callejas L., Shaid Sandoval-Miranda M.L., Zaldivar-Corichi A., “On Strongly Harmonic and Gelfand Modules”, Commun. Algebr., 48:5 (2020), 1985–2013  crossref  mathscinet  isi
    7. Beiranvand P.K., Beyranvand R., “Almost Prime and Weakly Prime Submodules”, J. Algebra. Appl., 18:7 (2019), 1950129  crossref  mathscinet  zmath  isi
    8. Groenewald N.J., Ssevviiri D., “Classical Completely Prime Submodules”, Hacet. J. Math. Stat., 45:3 (2016), 717–729  crossref  mathscinet  zmath  isi  scopus
    9. 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
    10. Jawad Abuhlail, “Zariski Topologies for Coprime and Second Submodules”, Algebra Colloq, 22:01 (2015), 47  crossref  mathscinet  zmath  scopus  scopus
    11. 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
    12. Jawad Abuhlail, “A Zariski Topology for Modules”, Communications in Algebra, 39:11 (2011), 4163  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Jawad Abuhlail, “A dual Zariski topology for modules”, Topology and its Applications, 158:3 (2011), 457  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. 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
    15. A. A. Tuganbaev, “Multiplication modules and ideals”, J Math Sci, 136:4 (2006), 4116  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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