⊕-Dual (Eş) Sonlu Radikal Tümlenmiş Modüllerin Genelleştirilmesi

Yıl 2024, , 36 - 43, 29.06.2024

Şeyma Haldız , Figen Eryılmaz

https://doi.org/10.33484/sinopfbd.1381635

Öz

Bu makalede ⊕−dual sonlu radikal tümleyen modüllerin genellemesi olarak maksimal alt modülleri ⊕−radikal tümleyene sahip modüller (𝑚𝑔𝑠⊕) tanımlandı ve bu modülün bazı temel özellikleri incelendi. Keyfi bir 𝑚𝑔𝑠⊕−modülünün bölüm modülünün hangi şartlar altında 𝑚𝑔𝑠⊕−modül olduğu gösterildi ve yarı mükemmel halkalar bu modül yardımıyla karakterize edildi.

Anahtar Kelimeler

Maksimal alt modül, radikal tümleyen, ⊕−dual sonlu radikal tümlenmiş modül

Generalization of ⊕-Cofinitely Radical Supplemented Modules

Öz

In this study, we clarify 𝑚𝑔𝑠⊕−modules that are the generalization of ⊕−cofinitely radical supplemented modules and look at some of their basic characteristics. Additionally, we determine the prerequisites for the factor module of an arbitrary 𝑚𝑔𝑠⊕−module to be a 𝑚𝑔𝑠⊕−module and characterized semiperfect rings with the aid of this module.

Anahtar Kelimeler

Maximal submodule, Rad-supplement, ⊕−cofinitely radical supplemented module

Kaynakça

• Wisbauer, R. (1991). Foundations of Module and Ring Theory. Gordon and Breach Science Publishing, Philadelphia.
• Eryılmaz, F. & Sözen, E. Ö. (2023). On a generalization of ⊕−co-coatomically supplemented modules. Honam Mathematical Journal, 45(1), 146-159. https://doi:10.5831/hmj.2023.45.1.146
• Sözen E. Ö. & Eren, Ş. (2018). Modules that have a generalized 𝛿−supplement in every cofinite extension. JP Journal of Algebra, Number Theory and Applications, 40(3), 241-254.
• Harmancı, A., Keskin, D. & Smith, P. F. (1999). On ⊕−supplemented modules. Acta Mathematica Hungarica, 83(1–2), 161–169.
• Çalışıcı, H. & Pancar, A. (2004).⊕−cofinitely supplemented modules. Czechoslovak Mathematical Journal, 54(129), 1083–1088.
• Clark, J., Lomp, C., Vajana, N. & Wisbauer, R. (2006). Lifting Modules. Birkhauser, Basel.
• Wang, Y. & Ding, N. (2006). Generalized supplemented modules. Taiwanese Journal of Mathematics, 10(6), 1589-1601.
• Büyükaşık, E. & Lomp,C. (2008). On a recent generalization of semiperfect rings. Bulletin of Australian Mathematical Society, 78, 317-325.
• Talebi, Y., Hamzekolaei, A. R. & Tütüncü, D. K. (2009). On Rad-⊕-supplemented modules. Hadronic Journal, 32(5), 505-512.
• Talebi, Y. & Mahmoudi, A. R. (2011). On Rad-⊕-supplemented modules. Thai Journal of Mathematics, 9(2), 373–381.
• Nişancı, B. & Pancar, A. (2010). On generalization of ⊕−cofinitely supplemented modules. Ukrainian Mathematical Journal, 62(2), 203-209, https://doi.org/10.1007/s11253-010-0344-4
• Koşan, M. T. (2009). Generalized cofinitely semiperfect modules. International Electronic Journal of Algebra, 5(5), 58-69.
• Mohamed, S. H & Müller, B. J. (1990). Continuous and Discrete Modules. Cambridge University Press, Cambridge.
• Garcia, J. L. (1989). Properties of direct summands of modules. Communications in Algebra, 17(1), 73-92, https://doi.org/10.1080/00927878908823714
• Özcan, A. Ç., Harmancı, A. & Smith, P. F. (2006). Duo modules. Glasgow Mathematical Journal, 48, 533-545, https://doi.org/10.1017/S0017089506003260