Öz
Kaynakça
- 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).
Öz
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 $R$.
Anahtar Kelimeler
Locally artinian module (Locally artinian) supplement (strongly) locally artinian radical supplemented module Left perfect ring Dedekind domain
Kaynakça
- 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).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Temmuz 2021 |
| Gönderilme Tarihi | 8 Temmuz 2021 |
| Kabul Tarihi | 29 Temmuz 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 4 Sayı: 2 |
