Proper classes generated by τ- closed submodules

[1] K. Al-Takhman, C. Lomp and R. Wisbauer: τ -complemented and τ -supplemented modules. Algebra Discrete Math. 3 (2006), 1–16.10.12988/ija.2007.07065Search in Google Scholar

[2] U. Albrecht: On the existence of maximal S-closed submodules. Rend. Semin. Mat. Univ. Padova 136 (2016), 277–289.10.4171/RSMUP/136-18Search in Google Scholar

[3] U. Albrecht, J. Dauns and L. Fuchs: Torsion-freeness and non-singularity over right p.p.-rings. J. Algebra 285 (2005), 98–119.10.1016/j.jalgebra.2004.10.020Search in Google Scholar

[4] D. A. Buchsbaum: A note on homology in categories. Ann. of Math. (2) 69 (1959), 66–74.10.2307/1970093Search in Google Scholar

[5] E. Büyükaşık and Y. Durğun: Absolutely s-pure modules and neat-flat modules. Comm. Algebra 43 (2015), 384–399.10.1080/00927872.2013.842246Search in Google Scholar

[6] E. Büyükaşık and Y. Durğun: Neat-flat Modules. Comm. Algebra. 44 (2016) , 416–428.10.1080/00927872.2014.982816Search in Google Scholar

[7] A. W. Chatters and S. M. Khuri: Endomorphism rings of modules over nonsingular CS rings. J. London Math. Soc. (2). 21 (1980), 434–444.10.1112/jlms/s2-21.3.434Search in Google Scholar

[8] J. Clark, C.Lomp, N.Vanaja and R. Wisbauer: Lifting modules. Birkhäuser Verlag, Basel 2006.Search in Google Scholar

[9] P. M. Cohn: On the free product of associative rings. Math. Z. 71 (1959), 380–398.10.1007/BF01181410Search in Google Scholar

[10] S. Crivei: Injective modules relative to torsion theories. EFES Publishing House, Cluj-Napoca, 2004.Search in Google Scholar

[11] S. Crivei and S. Şahinkaya: Modules whose closed submodules with essential socle are direct summands. Taiwanese J. Math. 18 (2014), 989–1002.10.11650/tjm.18.2014.3388Search in Google Scholar

[12] Y. Durğun: On some generalizations of closed submodules. Bull. Korean Math. Soc. 52 (2015), 1549–1557.10.4134/BKMS.2015.52.5.1549Search in Google Scholar

[13] Y. Durğun and S.Özdemir: On S-closed submodules. J. Korean Math. Soc. 54 (2017), 1281–1299.Search in Google Scholar

[14] L. Fuchs: Neat submodules over integral domains. Period. Math. Hungar. 64 (2012), 131–143.10.1007/s10998-012-7509-xSearch in Google Scholar

[15] J. S. Golan : Torsion theories. Longman Scientific & Technical, Harlow, 1986.Search in Google Scholar

[16] K. R. Goodearl: Singular torsion and the splitting properties. American Mathematical Society, Providence, R. I., 1972.10.1090/memo/0124Search in Google Scholar

[17] K. R. Goodearl: Ring theory. Marcel Dekker, Inc., New York-Base, 1976.Search in Google Scholar

[18] K. Honda: Realism in the theory of abelian groups. I. Comment. Math. Univ. St. Paul., 5 (1956), 37–75.Search in Google Scholar

[19] Y. Kara and A. Tercan: When some complement of a z-closed submodule is a summand, Comm. Algebra. 46 (2018), 3071–3078.10.1080/00927872.2017.1404080Search in Google Scholar

[20] T. Kepka: On one class of purities. Comment. Math. Univ. Carolinae 14 (1973), 139–154.Search in Google Scholar

[21] E. Mermut, C.Santa-Clara and P. F. Smith: Injectivity relative to closed submodules, J. Algebra 321 (2009), 548–557.10.1016/j.jalgebra.2008.11.004Search in Google Scholar

[22] A. Pancar: Generation of proper classes of short exact sequences. Internat. J. Math. Mat. Sci. 20 (1997), 465–473.10.1155/S016117129700063XSearch in Google Scholar

[23] G. Renault:Étude de certains anneaux A liés aux sous-modules compléments dun a-module. C. R. Acad. Sci. Paris, 259 (1964), 4203-4205.Search in Google Scholar

[24] F. L. Sandomierski: Nonsingular rings. Proc. Amer. Math. Soc. 19 (1968), 225–230.10.1090/S0002-9939-1968-0219568-5Search in Google Scholar

[25] E. G. Sklyarenko: Relative homological algebra in the category of modules. Uspehi Mat. Nauk. 33 (1978), 85–120.10.1070/RM1978v033n03ABEH002466Search in Google Scholar

[26] A. Tercan: On CLS-modules. Rocky Mountain J. Math. 25 (1995), 1557–1564.10.1216/rmjm/1181072161Search in Google Scholar

[27] J. Wang and D. Wu: When an S-closed submodule is a direct summand. Bull. Korean Math. Soc. 51 (2014), 613–619.10.4134/BKMS.2014.51.3.613Search in Google Scholar