Research Article

Strongly ⨁-Locally Artinian Supplemented Modules

Number: 28 November 30, 2021
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Strongly ⨁-Locally Artinian Supplemented Modules

Abstract

The aim of this paper is to investigate strong notion of strongly ⨁-supplemented modules in module theory, namely strongly ⨁-locally artinian supplemented modules. We call a module M strongly ⨁-locally artinian supplemented if it is locally artinian supplemented and its locally artinian supplement submodules are direct summand. In this study, we provide the basic properties of strongly ⨁-locally artinian supplemented modules. In particular, we show that every direct summand of a strongly ⨁-locally artinian supplemented module is strongly ⨁-locally artinian supplemented. Moreover, we prove that a ring R is semiperfect with locally artinian radical if and only if every projective R-module is strongly ⨁-locally artinian supplemented.

Keywords

References

  1. Clark, J., Lomp, C., Vanaja, N., & Wisbauer, R.. (2012). Lifting Modules Supplements and Projectivity in Module Theory. Basel. Boston. Berlin, Birkhauser Verlag.
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  4. Kaynar, E. , Çalışıcı, H., Türkmen, E. (2020). SS-supplemented modules. Communications Faculty of Science University of Ankara Series A1 Mathematics and statistics, 69(1):473-485.
  5. Nebiyev, C., & Pancar, A. (2011). On strongly ⨁-supplemented modules. Ukrainian Math.J., 63(5): 662-667.
  6. Sharpe, D.W., & Vamos, P. (1972). Injective Modules. Cambridge University Press, Cambridge.
  7. Şahin, Y., & Nişancı Türkmen, B. (2020). Locally artinian supplemented modules. 9th International Eurasian Conference On Mathematical Sciences and Applications Abstract Book, 26.
  8. Wisbauer, R. (1991). Foundations of Modules and Rings. Gordon and Breach, Springer-Verlag.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Publication Date

November 30, 2021

Submission Date

October 14, 2021

Acceptance Date

October 14, 2021

Published in Issue

Year 2021 Number: 28

DOI

https://doi.org/10.31590/ejosat.1009452

IZ

https://izlik.org/JA96WP46SB

Cite

RIS / Bibtex
APA
Nişancı Türkmen, B. (2021). Strongly ⨁-Locally Artinian Supplemented Modules. Avrupa Bilim Ve Teknoloji Dergisi, 28, 590-593. https://doi.org/10.31590/ejosat.1009452
AMA
1.Nişancı Türkmen B. Strongly ⨁-Locally Artinian Supplemented Modules. EJOSAT. 2021;(28):590-593. doi:10.31590/ejosat.1009452
Chicago
Nişancı Türkmen, Burcu. 2021. “Strongly ⨁-Locally Artinian Supplemented Modules”. Avrupa Bilim Ve Teknoloji Dergisi, nos. 28: 590-93. https://doi.org/10.31590/ejosat.1009452.
EndNote
Nişancı Türkmen B (November 1, 2021) Strongly ⨁-Locally Artinian Supplemented Modules. Avrupa Bilim ve Teknoloji Dergisi 28 590–593.
IEEE
[1]B. Nişancı Türkmen, “Strongly ⨁-Locally Artinian Supplemented Modules”, EJOSAT, no. 28, pp. 590–593, Nov. 2021, doi: 10.31590/ejosat.1009452.
ISNAD
Nişancı Türkmen, Burcu. “Strongly ⨁-Locally Artinian Supplemented Modules”. Avrupa Bilim ve Teknoloji Dergisi. 28 (November 1, 2021): 590-593. https://doi.org/10.31590/ejosat.1009452.
JAMA
1.Nişancı Türkmen B. Strongly ⨁-Locally Artinian Supplemented Modules. EJOSAT. 2021;:590–593.
MLA
Nişancı Türkmen, Burcu. “Strongly ⨁-Locally Artinian Supplemented Modules”. Avrupa Bilim Ve Teknoloji Dergisi, no. 28, Nov. 2021, pp. 590-3, doi:10.31590/ejosat.1009452.
Vancouver
1.Burcu Nişancı Türkmen. Strongly ⨁-Locally Artinian Supplemented Modules. EJOSAT. 2021 Nov. 1;(28):590-3. doi:10.31590/ejosat.1009452