Dual Sonlu Yarı Basit Yükseltilebilir Modüller

Yıl 2023, Cilt: 28 Sayı: 2, 424 - 431, 31.08.2023

Figen Eryılmaz

https://doi.org/10.53433/yyufbed.1143435

Öz

$N\,P-$modülünün dual sonlu her $S$ alt modülü $N=U'\oplus V,\,\,U'\subseteq S$ve $S\cap V\subseteq Soc_{s}(V)$olacak şekilde bir ayrışıma sahip ise $N\,R-$modülüne dual sonlu yarı basit yükseltilebilir modül veya kısaca dual sonlu ss-yükseltilebilir modül denir. Bu çalışmada, bu tanıma denk koşullar verilmiştir. Buna ek olarak, makalede tanımlanan bu kavramın basit özellikleri incelenmiştir.

Anahtar Kelimeler

Dual sonlu ss-yükseltilebilir modül, ss-tümlenmiş modül, Yarı basit modül

Cofinitely Semisimple (ss-) Lifting Modules

Öz

An $P-$module $N$ is named cofinitely semisimple lifting or briefly cofinitely $ss-$lifting if for each cofinite submodule $S$ of $N$, $N$ has a decomposition $N=U'\oplus V$ such that $U'\subseteq S$ and $S\cap V\subseteq Soc_{s}(V)$. In this study, equivalent conditions to this definition are given. In addition, the basic features of this concept defined in this article are examined.

Anahtar Kelimeler

Cofinitely ss-lifting module, Semisimple module, ss-supplemented module

Kaynakça

• Eryılmaz, F. (2021). SS-lifting modules and rings. Miskolc Mathematical Notes, 22(2), 655-662. doi:10.18514/mmn.2021.3245
• Kasch, F. (1982). Modules and Rings. London, UK: Academic Press Inc.
• Kaynar, E., Turkmen, E., & Çalışıcı, H. (2020). SS-supplemented modules. Communications Faculty of Sciences, University of Ankara, Series A1, Mathematics and Statistics, 69(1), 473 485. doi:10.31801/cfsuasmas.585727
• Keskin, D. (2000). On lifting modules. Communications in Algebra, 28(7),3427-3440. doi:10.1080/00927870008827034
• Mohamed, S. H., & Müller, B. J. (1990). Continuous and Discrete Modules. Cambridge, England: Cambridge University Press.
• Türkmen, B. N., & Türkmen, E. (2020). supplemented modules and rings. Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică, 28(3), 193-216. doi:10.2478/auom-2020-0041
• Türkmen, B. N., & Kılıç, B. (2022). On cofinitely ss-supplemented modules. Algebra and Discrete Mathematics, 34(1), 141-151. doi:10.12958/adm1668
• Tribak, R. (2008). On cofinitely lifting and cofinitely weak lifting modules. Communications in Algebra, 36(12), 4448-4460. doi:10.1080/00927870802179552
• Sözen, E. Ö. (2022). A study on Ss-semilocal modules in view of singularity. Malaya Journal of Matematik, 10(1), 90-97. doi:10.26637/mjm1001/008
• Özcan, A. Ç., Harmancı, A., & Smith, P. F. (2006). Duo modules. Glasgow Mathematical Journal, 48(3), 533-545. doi:10.1017/S0017089506003260
• Wang, Y. & Wu, D. (2010). On cofinitely lifting modules. Algebra Colloquium, 17(4), 659-666. doi:10.1142/S1005386710000635
• Wisbauer, R. (1991). Foundations of Module and Ring Theory. London, UK: Routledge. doi:10.1201/9780203755532
• Zhou, D. X., & Zhang, X. R. (2011). Small-essential submodules and morita duality. Southeast Asian Bulletin of Mathematics, 35(6), 1051-1062.
• Zöschinger, H. (1974). Komplementierte moduln uber dedekindringen. Journal of Algebra, 29, 42-56.