We define (strongly) t-radical supplemented modules and study some properties of these modules. These modules lie between strongly radical supplemented and strongly ⊕-radical supplemented modules. We also study the relationship between these modules and present examples separating strongly t-radical supplemented modules, supplemented modules, and strongly ⊕-radical supplemented modules.
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References
R. Alizade, G. Bilhan, and P. F. Smith, “Modules whose maximal submodules have supplements,” Comm. Algebra, 29, No. 6, 2389–2405 (2001).
E. Büyükaşık and C. Lomp, “On a recent generalization of semiperfect rings,” Bull. Aust. Math. Soc., 78, No. 2, 317–325 (2008).
E. Büyükaşık, E. Mermut, and S. Özdemir, “Rad supplemented modules,” Rend. Semin. Mat. Univ. Padova, 124, 157–177 (2010).
E. Büyükaşık and E. Türkmen, “Strongly radical supplemented modules,” Ukr. Math. J., 63, No. 8, 1306–1313 (2012).
J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, “Lifting modules, supplements, and projectivity in module theory,” Front. Math., Birkhäuser, Basel (2006).
H. Ҫalışıcı and E. Türkmen, “Generalized ⊕-supplemented modules,” Algebra Discrete Math., 10, 10–18 (2010).
A. Idelhadj and R. Tribak, “On some properties of ⊕-supplemented modules,” Int. J. Math. Math. Sci., 69, 4373–4387 (2003).
B. Kosar and C. Nebiyev, “tan-Supplemented modules,” Miskolc Math. Notes, 16, No. 2, 979–986 (2015).
S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, Cambridge Univ. Press (1990), 147.
Y. Talebi, A. R. M. Hamzekolaei, and D. K. Tütüncü, “On Rad ⊕-supplemented modules,” Hadronic J., 32, 505–512 (2009).
Y. Talebi and A. Mahmoudi, “On Rad ⊕-supplemented modules,” Thai J. Math., 9, No. 2, 373–381 (2011).
B. N. Türkmen and A. Pancar, “Generalizations of ⊕-supplemented modules,” Ukr. Math. J., 65, No. 4, 555–564 (2013).
Y. Wang and N. Ding, “Generalized supplemented modules,” Taiwanese J. Math., 10, No. 6, 1589–1601 (2006).
R. Wisbauer, Foundations of Module and Ring Theory, Gordon & Breach, Philadelphia (1991).
W. Xue, “Characterization of semiperfect and perfect rings,” Publ. Mat., 40, No. 1, 115–125 (1996).
H. Zӧschinger, “Komplementierte Moduln über Dedekindringen,” J. Algebra, 29, 42–56 (1974).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 9, pp. 1191–1196, September, 2016.
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Koşar, B., Nebiyev, C. T -Radical and Strongly T -Radical Supplemented Modules. Ukr Math J 68, 1366–1373 (2017). https://doi.org/10.1007/s11253-017-1301-2
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DOI: https://doi.org/10.1007/s11253-017-1301-2