On tau-discrete modules

Yıl 2024, , 37 - 43, 28.03.2024

Burcu Nişancı Türkmen , Ergül Türkmen

https://doi.org/10.18185/erzifbed.1251658

Öz

An R-module M is said to be (quasi) τ-discrete if M is τ-lifting and has the property (D_2) (respectively, has the property (D_3)), where τ is a preradical in R-mod. It is shown that: (1) direct summands of a (quasi) τ-discrete module are (quasi) τ-discrete; (2) a projective module M is τ-discrete iff M/(τ(M)) is semisimple and τ(M) is QSL; (3) if a projective module M is Soc-lifting, then M/(Soc(M)) is Soc-discrete and Rad(M/Soc(M) ) is semisimple.

Anahtar Kelimeler

preradical, τ-lifting mdule, (quasi) τ-discrete module.

Destekleyen Kurum

This work was presented in 3rd International Conference on Engineering and Applied Natural Sciences (ICEANS 2023) on 14-17 January in 2023 at Konya/Turkey.

Kaynakça

• [1] Al-Khazzi, I., and Smith, P.F., (1991) Modules with chain conditions on superfluous submodules, Communications in Algebra, Vol. 19(8), pp. 2331-2351.
• [2] Al-Takhman, K., Lomp, C. and Wisbauer, R. (2006) τ-complement and τ-supplement submodules, Algebra and Discrete Mathematics, 3, 1-15.
• [3] Alkan, M. (2009) On τ-lifting modules and τ-semiperfect modules, Turkish Journal of Mathematics, 33(2), 117-130.
• [4] Büyükaşık, E., Mermut, E. and Özdemir, S. (2010) Rad-supplemented modules, Rendiconti del Seminario Matematico della Universita di Padova, 124, 157-177.
• [5] Mohamed S.H. and Müller, B.J. (1990) Continuous and Discrete Modules”, London Mathematical Society, LNS 147 Cambridge University Press, Cambridge.
• 6] Nicholson, W.K. and Zhou, Y. (2005) Strongly lifting, Journal of Algebra, 285, 795-818.
• [7] Nişancı Türkmen, B., Ökten, H.H. and Türkmen, E. (2021) Rad-discrete Modules, Bulletin of the Iranian Mathematical Society, 47, 91-100.
• [8] Türkmen, E. (2013) Rad-⨁-supplemented modules”, Analele Stiintifice ale Universitatii Ovidius Constanta Seria Mathematica, 21 (1), 225-238.
• [9] Wisbauer, R. (1991) Foundations of Module and Ring Theory (A handbook for study and research)”, Gordon and Breach Science Publishers.