Some Generalizations of g-lifting Modules
DOI:
https://doi.org/10.29304/jqcm.2023.15.1.1173Keywords:
g-lifting module, ⨁-g-supplemented module, ⨁-g-radical supplemented module, g-semiperfect module, (〖P_g〗^*) propertyAbstract
In this work we will attempt to define and investigate new classes of modules named -g-supplemented and -g-radical supplemented as a proper generalization of class of g-lifting modules and identify several distinct characterizations of these modules. Additionally, we'll attempt to explain the concepts of projective g-covers and g-semiperfect modules. It is shown that the two buildings of g-semiperfect and -g-supplemented modules are the same for the class of projective modules.
Downloads
Download data is not yet available.
References
[1] Y. Zhou, Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq., 7(3)(2000), p.305-3018.
[2] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.
[3] M. T. Kosan, δ-lifting and δ-supplemented modules, Algebra Colloq., 14(1)(2007), p.53-60.
[4] W. Xue, Characterizations of semiperfect and perfect rings, Publications Matemàtiques, 40(1996), p.115-125.
[5] Y. Talebi and B. Talaee, On generalized δ-supplemented modules, Vietnam J. Math., 37(4)(2009), p.515-525.
[6] D. X. Zhou and X. R. Zhang, Small-essential submodules and morita duality, Southeast Asian Bull. Math., 35(2011), p.1051-1062.
[7] B. Koşar, C. Nebiyev and N. Sökmez, G-supplemented modules, Ukrainian Mathematical Journal, 67(6)(2015), p.861-864.
[8] T. C. Quynh and P. H. Tin, Some properties of e-supplemented and e-lifting modules, Vietnam J. Math., 41(3)( 2013), p.303-312.
[9] B. Koşar, C. Nebiyev and A. Pekin, A generalization of G-supplemented modules, Miskolc Mathematical Notes, 20(1)(2019), p.345-352.
[10] S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Math. Soc. Lecture Note Series, 147, Cambridge University press,
1990.
[11] A. Harmanci, D. Keskin and P. F. Smith, On ⨁-supplemented modules, Acta Math. Hungar., 83(1-2)(1999), p.161-169.
[12] Y. Talebi and M. H. Pour, On ⨁-δ-supplemented modules, J. of Algebra, Number Theory, Adv. and Appl., 1(2)(2009), p.89-97.
[13] S. Ecevit, M. T. Kosan and R. Tribak, Rad-⨁-supplemented modules and cofinitely Rad-⨁-supplemented modules, Algebra Colloq., 19(4)(2012),
p.637-648.
[14] F. Y. Eryilmaz and S. Eren, Generalization of ⨁-δ-supplemented modules, Int. J. of Algebra, 6(27)(2012), p.1303-1308.
[15] W. Khalid and A. S. Wadi, Generalized radical lifting modules, Iraqi Journal of Science, Vol. 58, No. 2C, 2017, p.1107-1111.
[16] A. Ali and W. Khalid, FI-⨁-J-supplemented modules, Iraqi Journal of Science, Vol. 62, No. 5(2021), p.1637-1634.
[17] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1974.
[18] L. V. Thuyet, Some Characterizations of modules via essentially small submodules, Kyungpook Math. J., 56(2010), p.1069-1083.
[19] D. Keskin and W. Xue, Generalizations of lifting modules, Acta Math. Hungar., 91(3)(2001), p.253-261.
[20] A. C. Özcan, A. Harmanci and P. F. Smith, Duo modules, Glasgow Math. J., 48(3)(2006), p.533-545.
[21] V. Camillo, Distributive modules, J. of Algebra, 36(1975), p. 16-25.
[22] J. M. Zelmanowitz, Representation of rings with faithful polyform modules, Comm. Algebra, 14(1986), p.1141-1169.
[23] M. Alkan and A. Harmanci, On summand sum and summand intersection property of Modules, Turk. J. Math., 26(2002), p.131-147.
[24] K. Varadarajan, Dual Goldie dimension, Comm. Algebra, 7(6)(1979), p.565-610.
[2] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.
[3] M. T. Kosan, δ-lifting and δ-supplemented modules, Algebra Colloq., 14(1)(2007), p.53-60.
[4] W. Xue, Characterizations of semiperfect and perfect rings, Publications Matemàtiques, 40(1996), p.115-125.
[5] Y. Talebi and B. Talaee, On generalized δ-supplemented modules, Vietnam J. Math., 37(4)(2009), p.515-525.
[6] D. X. Zhou and X. R. Zhang, Small-essential submodules and morita duality, Southeast Asian Bull. Math., 35(2011), p.1051-1062.
[7] B. Koşar, C. Nebiyev and N. Sökmez, G-supplemented modules, Ukrainian Mathematical Journal, 67(6)(2015), p.861-864.
[8] T. C. Quynh and P. H. Tin, Some properties of e-supplemented and e-lifting modules, Vietnam J. Math., 41(3)( 2013), p.303-312.
[9] B. Koşar, C. Nebiyev and A. Pekin, A generalization of G-supplemented modules, Miskolc Mathematical Notes, 20(1)(2019), p.345-352.
[10] S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Math. Soc. Lecture Note Series, 147, Cambridge University press,
1990.
[11] A. Harmanci, D. Keskin and P. F. Smith, On ⨁-supplemented modules, Acta Math. Hungar., 83(1-2)(1999), p.161-169.
[12] Y. Talebi and M. H. Pour, On ⨁-δ-supplemented modules, J. of Algebra, Number Theory, Adv. and Appl., 1(2)(2009), p.89-97.
[13] S. Ecevit, M. T. Kosan and R. Tribak, Rad-⨁-supplemented modules and cofinitely Rad-⨁-supplemented modules, Algebra Colloq., 19(4)(2012),
p.637-648.
[14] F. Y. Eryilmaz and S. Eren, Generalization of ⨁-δ-supplemented modules, Int. J. of Algebra, 6(27)(2012), p.1303-1308.
[15] W. Khalid and A. S. Wadi, Generalized radical lifting modules, Iraqi Journal of Science, Vol. 58, No. 2C, 2017, p.1107-1111.
[16] A. Ali and W. Khalid, FI-⨁-J-supplemented modules, Iraqi Journal of Science, Vol. 62, No. 5(2021), p.1637-1634.
[17] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1974.
[18] L. V. Thuyet, Some Characterizations of modules via essentially small submodules, Kyungpook Math. J., 56(2010), p.1069-1083.
[19] D. Keskin and W. Xue, Generalizations of lifting modules, Acta Math. Hungar., 91(3)(2001), p.253-261.
[20] A. C. Özcan, A. Harmanci and P. F. Smith, Duo modules, Glasgow Math. J., 48(3)(2006), p.533-545.
[21] V. Camillo, Distributive modules, J. of Algebra, 36(1975), p. 16-25.
[22] J. M. Zelmanowitz, Representation of rings with faithful polyform modules, Comm. Algebra, 14(1986), p.1141-1169.
[23] M. Alkan and A. Harmanci, On summand sum and summand intersection property of Modules, Turk. J. Math., 26(2002), p.131-147.
[24] K. Varadarajan, Dual Goldie dimension, Comm. Algebra, 7(6)(1979), p.565-610.
Downloads
Published
2023-04-03
How to Cite
Ghawi, T. Y. (2023). Some Generalizations of g-lifting Modules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(1), Math Page 109–121. https://doi.org/10.29304/jqcm.2023.15.1.1173
Issue
Section
Math Articles
