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Year 2021, Volume: 4 Issue: 2, 252 - 258, 31.07.2021

Burcu Nişancı Türkmen

https://doi.org/10.33773/jum.967960

Abstract

References

  • Referans1 R. Alizade, G. Bilhan, P. F. Smith. Modules whose maximal submodules have supplements. Communications in Algebra, Vol. 29(6), pp. 2389-2405 (2001).
  • Referans2 E. Büyükaşık, E. Türkmen. Strongly radical supplemented modules. Ukr. Math. J., 63, No. 8, 1306-1313 (2011).
  • Referans3 C. Faith. Rings whose modules have maximal submodules. Publicacions Mathematiques, Vol. 39, pp. 201-214 (1995).
  • Referans4 E. Kaynar, H. Çalışıcı, E. Türkmen. ss-supplemented modules. Communications Faculty of Science University of Ankara Series A1 Mathematics and statistics, Vol. 69, 1, pp 473-485 (2020).
  • Referans5 S. H. Mohamed and B. J. Müller. Continuous and discrete modules. London Math. Soc., Lect. Note Ser., 147 (1990).
  • Referans6 B. Nişancı Türkmen, A. Pancar. On generalizations of $\oplus$-supplemented modules. Ukrainian Mathematical Journal, Vol. 65(4) pp. 612-622 (2013).
  • Referans7 D. W. Sharpe, P. Vamos. Injective modules. Cambridge University Press, Cambridge, (1972).
  • Referans8 Y. Şahin, B. Nişancı Türkmen. Locally-artinian supplemented modules. 9th International Eurasian Conference On Mathematical Sciences and Applications Abstract Book,Skopje, North Macedonia, pp. 26 (2020).
  • Referans9 R. Wisbauer. Foundations of modules and rings. Gordon and Breach, Springer-Verlag (1991).
  • Referans10 D. X. Zhou, X. R. Zhang. Small-essential submodules and morita duality. Southeast Asian Bulletin of Mathematics, Vol. 35, pp 1051-1062 (2011).
  • Referans11 H. Zöschinger. Moduln, die in jeder erweiterung ein komplement haben. Mathematica Scandinavica, Vol. 35, pp. 267-287 (1974).
  • Referans12 H. Zöschinger. Komplementierte moduln über dedekindringen. Journal of Algebra, Vol. 29, pp. 42-56 (1974).
  • Referans13 H. Zöschinger. Basis-untermoduln und quasi-kotorsions-moduln ber diskreten bewertungsringen. Bayer. Akad. Wiss. Math. Natur. Kl., Vol. 2, pp. 9-16 (1976).

ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES

Year 2021, Volume: 4 Issue: 2, 252 - 258, 31.07.2021

Burcu Nişancı Türkmen

https://doi.org/10.33773/jum.967960

Abstract

The aim of this paper is to investigate generalizations of locally artinian supplemented modules in module theory, namely locally artinian radical supplemented modules and strongly locally artinian radical supplemented modules. We have obtained elementary features for them. Also, we have characterized strongly locally artinian radical supplemented modules by left perfect rings. Finally, we have proved that the reduced part of a strongly locally artinian radical supplemented $R$-module has the same property over a Dedekind domain $R$.

Keywords

Locally artinian module (Locally artinian) supplement (strongly) locally artinian radical supplemented module Left perfect ring Dedekind domain

References

  • Referans1 R. Alizade, G. Bilhan, P. F. Smith. Modules whose maximal submodules have supplements. Communications in Algebra, Vol. 29(6), pp. 2389-2405 (2001).
  • Referans2 E. Büyükaşık, E. Türkmen. Strongly radical supplemented modules. Ukr. Math. J., 63, No. 8, 1306-1313 (2011).
  • Referans3 C. Faith. Rings whose modules have maximal submodules. Publicacions Mathematiques, Vol. 39, pp. 201-214 (1995).
  • Referans4 E. Kaynar, H. Çalışıcı, E. Türkmen. ss-supplemented modules. Communications Faculty of Science University of Ankara Series A1 Mathematics and statistics, Vol. 69, 1, pp 473-485 (2020).
  • Referans5 S. H. Mohamed and B. J. Müller. Continuous and discrete modules. London Math. Soc., Lect. Note Ser., 147 (1990).
  • Referans6 B. Nişancı Türkmen, A. Pancar. On generalizations of $\oplus$-supplemented modules. Ukrainian Mathematical Journal, Vol. 65(4) pp. 612-622 (2013).
  • Referans7 D. W. Sharpe, P. Vamos. Injective modules. Cambridge University Press, Cambridge, (1972).
  • Referans8 Y. Şahin, B. Nişancı Türkmen. Locally-artinian supplemented modules. 9th International Eurasian Conference On Mathematical Sciences and Applications Abstract Book,Skopje, North Macedonia, pp. 26 (2020).
  • Referans9 R. Wisbauer. Foundations of modules and rings. Gordon and Breach, Springer-Verlag (1991).
  • Referans10 D. X. Zhou, X. R. Zhang. Small-essential submodules and morita duality. Southeast Asian Bulletin of Mathematics, Vol. 35, pp 1051-1062 (2011).
  • Referans11 H. Zöschinger. Moduln, die in jeder erweiterung ein komplement haben. Mathematica Scandinavica, Vol. 35, pp. 267-287 (1974).
  • Referans12 H. Zöschinger. Komplementierte moduln über dedekindringen. Journal of Algebra, Vol. 29, pp. 42-56 (1974).
  • Referans13 H. Zöschinger. Basis-untermoduln und quasi-kotorsions-moduln ber diskreten bewertungsringen. Bayer. Akad. Wiss. Math. Natur. Kl., Vol. 2, pp. 9-16 (1976).
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Burcu Nişancı Türkmen 0000-0001-7900-0529

Publication Date July 31, 2021
Submission Date July 8, 2021
Acceptance Date July 29, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Nişancı Türkmen, B. (2021). ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES. Journal of Universal Mathematics, 4(2), 252-258. https://doi.org/10.33773/jum.967960
AMA Nişancı Türkmen B. ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES. JUM. July 2021;4(2):252-258. doi:10.33773/jum.967960
Chicago Nişancı Türkmen, Burcu. “ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES”. Journal of Universal Mathematics 4, no. 2 (July 2021): 252-58. https://doi.org/10.33773/jum.967960.
EndNote Nişancı Türkmen B (July 1, 2021) ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES. Journal of Universal Mathematics 4 2 252–258.
IEEE B. Nişancı Türkmen, “ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES”, JUM, vol. 4, no. 2, pp. 252–258, 2021, doi: 10.33773/jum.967960.
ISNAD Nişancı Türkmen, Burcu. “ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES”. Journal of Universal Mathematics 4/2 (July 2021), 252-258. https://doi.org/10.33773/jum.967960.
JAMA Nişancı Türkmen B. ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES. JUM. 2021;4:252–258.
MLA Nişancı Türkmen, Burcu. “ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES”. Journal of Universal Mathematics, vol. 4, no. 2, 2021, pp. 252-8, doi:10.33773/jum.967960.
Vancouver Nişancı Türkmen B. ON GENERALIZATIONS OF LOCALLY ARTINIAN SUPPLEMENTED MODULES. JUM. 2021;4(2):252-8.
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