Öz
Bu çalışmanın amacı 〖FI〗_ss-yükseltilebilir ve güçlü 〖FI〗_ss-yükseltilebilir modüllerin bazı temel özelliklerini göstermektir. (Güçlü) 〖FI〗_ss-yükseltilebilir modüllerin direkt toplam terimlerinin, direkt toplamlarının ve alt modüllerinin hangi koşullar altında altında (güçlü) 〖FI〗_ss-yükseltilebilir modül olduğunu inceliyoruz. FI-yükseltilebilir bir modülün 〖FI〗_ss-yükseltilebilir olmak zorunda olmadığını gösteren bir örnek veriyoruz. Güçlü 〖FI〗_ss-yükseltilebilir modül olma özelliğinin direkt toplam terimleri tarafından aktarıldığını ispatlıyoruz.
Anahtar Kelimeler
ss-tümleyen alt modül 〖FI〗_ss-yükseltilebilir modül güçlü 〖FI〗_ss-yükseltilebilir modül
Kaynakça
- Birkenmeier, G. F., Müller, B. J., Rizvi, S. T., (2002). Modules in Which Every Fully Invariant Submodule is Essential in a Direct Summand. Communications in Algebra, 30(3), 1395-1415.
- Clark, J., Lomp, C., Vanaja, N., Wisbauer, R., (2006). Lifting modules. Birkhauser, Verlag-Basel: Frontiers In Mathematics.
- Eryılmaz, F., (2021). ss-Lifting Modules and Rings. Miskolc Mathematical Notes, 22(2), 655-662.
- Garcia, J. L., (1989). Properties of Direct Summands of Modules. Communications in Algebra, 17(1), 73-92.
- Kasch, F., (1982). Modules and rings. Teubner: Published for the London Mathematical Society by Academic Press.
- Kaynar, E., Çalışıcı, H., Türkmen, E., (2020). ss-Supplemented Modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69 (1), 473-485.
- Koşan, M. T., (2005). The Lifting Condition and Fully Invariant Submodules. East-West Journal of Mathematics, 7(1), 99-106.
- Nişancı Türkmen, B., (2020). Weak ss-Lifting Modules. American Scientific Research Journal for Engineering, Technology and Sciences, 74(1), 232-236.
- Özcan, A. Ç., Harmancı, A., Smith, P. F., (2006). Duo Modules. Glasgow Mathematical Journal, 48(3), 533-545.
- Öztürk Sözen, E. (2020). Bol e-Tümlenmiş Modüllere ve e-Yükseltilebilir Modüllere Torsiyon-Teorik Bir Yaklaşım. Erzincan University Journal of Science and Technology, 13(2), 592-599.
- Rizvi, S. T., Cosmin, S. R., (2004). Baer and Quasi-Baer Modules. Communications in Algebra, 32, 103-123.
- Talebi, Y., Vanaja, N., (2002). The Torsion Theory Cogenerated by M-Small Modules. Communications in Algebra, 30(3), 1449-1460.
- Talebi, Y., Amoozegar, T., (2008). Strongly FI-Lifting Modules. International Electronic Journal of Algebra, 3, 75-82.
- Tian, J., Öztürk Sözen, E., Moniri Hamzekolaee, A. R. (2023). Some Variations of 𝛿-Supplemented Modules with Regard to a Hereditary Torsion Theory. Journal of Mathematics, Article ID 9968793, 7p.
- Wisbauer, R., (1991). Foundations of module and ring theory. Gordon and Breach, Philedelphia: Gordon and Breach Science Publishers.
- Zhou, D. X., Zhang, X. R., (2011). Small-Essential Submodules and Morita Duality. Southeast Asian Bulletin of Mathematics, 35(6), 1051–1062.
Öz
The purpose of this note is to show some key features of 〖FI〗_ss-lifting and strongly 〖FI〗_ss-lifting modules. We examine that under whose condition for direct summands, direct sums and submodules of (strongly) 〖FI〗_ss-lifting modules are (strongly) 〖FI〗_ss-lifting. We give an example to exhibit that an FI-lifting module needs not to be 〖FI〗_ss-lifting. We provide that the property of being strongly 〖FI〗_ss-lifting module is inherited by direct summands.
Anahtar Kelimeler
ss-supplement submodule 〖FI〗_ss-lifting module strongly 〖FI〗_ss-lifting module
Kaynakça
- Birkenmeier, G. F., Müller, B. J., Rizvi, S. T., (2002). Modules in Which Every Fully Invariant Submodule is Essential in a Direct Summand. Communications in Algebra, 30(3), 1395-1415.
- Clark, J., Lomp, C., Vanaja, N., Wisbauer, R., (2006). Lifting modules. Birkhauser, Verlag-Basel: Frontiers In Mathematics.
- Eryılmaz, F., (2021). ss-Lifting Modules and Rings. Miskolc Mathematical Notes, 22(2), 655-662.
- Garcia, J. L., (1989). Properties of Direct Summands of Modules. Communications in Algebra, 17(1), 73-92.
- Kasch, F., (1982). Modules and rings. Teubner: Published for the London Mathematical Society by Academic Press.
- Kaynar, E., Çalışıcı, H., Türkmen, E., (2020). ss-Supplemented Modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69 (1), 473-485.
- Koşan, M. T., (2005). The Lifting Condition and Fully Invariant Submodules. East-West Journal of Mathematics, 7(1), 99-106.
- Nişancı Türkmen, B., (2020). Weak ss-Lifting Modules. American Scientific Research Journal for Engineering, Technology and Sciences, 74(1), 232-236.
- Özcan, A. Ç., Harmancı, A., Smith, P. F., (2006). Duo Modules. Glasgow Mathematical Journal, 48(3), 533-545.
- Öztürk Sözen, E. (2020). Bol e-Tümlenmiş Modüllere ve e-Yükseltilebilir Modüllere Torsiyon-Teorik Bir Yaklaşım. Erzincan University Journal of Science and Technology, 13(2), 592-599.
- Rizvi, S. T., Cosmin, S. R., (2004). Baer and Quasi-Baer Modules. Communications in Algebra, 32, 103-123.
- Talebi, Y., Vanaja, N., (2002). The Torsion Theory Cogenerated by M-Small Modules. Communications in Algebra, 30(3), 1449-1460.
- Talebi, Y., Amoozegar, T., (2008). Strongly FI-Lifting Modules. International Electronic Journal of Algebra, 3, 75-82.
- Tian, J., Öztürk Sözen, E., Moniri Hamzekolaee, A. R. (2023). Some Variations of 𝛿-Supplemented Modules with Regard to a Hereditary Torsion Theory. Journal of Mathematics, Article ID 9968793, 7p.
- Wisbauer, R., (1991). Foundations of module and ring theory. Gordon and Breach, Philedelphia: Gordon and Breach Science Publishers.
- Zhou, D. X., Zhang, X. R., (2011). Small-Essential Submodules and Morita Duality. Southeast Asian Bulletin of Mathematics, 35(6), 1051–1062.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 18 Haziran 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 14 Sayı: 2 |
Karadeniz Fen Bilimleri Dergisinde yayınlanan makaleler Creative Commons Attribution-NonCommercial 4.0 International
kapsamında lisanslanmıştır.