Principally ⨁-g-supplemented modules
DOI:
https://doi.org/10.29304/jqcm.2022.14.1.906Keywords:
g-small submodules, principally g-supplemented modules, principally ⨁-g-supplemented modules, principally g-lifting modules, principally semisimple modulesAbstract
In this paper, we defined and studied the idea of principally -g-supplemented modules as an advanced concept of -g-supplemented modules. Many properties, characterizations and examples of these modules are discussed. Also, a number of relations between these modules and other kinds of modules are examined in this work.
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References
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1069-1083.
[20] A. Tuganbaev, Semi distributive modules and rings, Kluwer Academics Publishers, Dordrecht, 1998.
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Contemporary Mathematics, Amer. Math. Soc., 2014, 123–136.
[22] B. Ungor, S. Halicioglu and A. Harmanci, On a class of δ-supplemented modules, Bull. Malays. Math. Sci. Soc., 37(3)(2014),
703-717.
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and Applied Mathematics, 81, Longman, Harlow. MR1396313 (97i:16002), 1996.
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1051-1062.
[2] R. Alizade, G. Bilhan and Smith PF. Modules whose maximal submodules have supplements, Communications in Algebra, 29(6)
(2001), 2389-2405.
[3] M. Alkan, A. Harmanci: On summand sum and summand intersection property of modules, Turk. J. Math., 26(2002), 131-147.
[4] E. Büyükaşik and Y. Demirci, Weakly distributive modules, Applications to supplement submodules, Proc. Indian Acad. Sci.
(Math. Sci.), 120(2010), 525-534.
[5] V. Camillo, Distributive modules, J. of Algebra, 36(1975), 16-25.
[6] J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting modules, supplements and projectivity in module theory, Frontiers in
Mathematics, Birkhäuser Verlag, Basel, 2006.
[7] N.V. Dung, D.V. Huyn, P.F. Smith and R. Wisbauer, Extending modules, Pitman Research notes in math. Series, 313, Longman
Scientific and Technical: Harlow, 1994.
[8] T. Y. Ghawi, On a class of g-lifting modules, Journal of Discrete Mathematical Sciences & Cryptography, 24(6)(2021), 1857-1872.
[9] T. Y. Ghawi, Some generalizations of g-lifting modules, Quasigroups and Related Systems, 2022, to appear.
[10] K. R. Goodearl, Ring theory, Nonsingular rings and modules, Dekker, Newyork, 1976.
[11] I. Hatice, H. Sait and A. Harmanci, A generalization of supplemented modules, Algebra and Discrete Mathematics, 11(1)(2011),
59-74.
[12] F. Kasch, Modules and rings module, New York, 1982.
[13] D. Keskin and W. Xue, Generalizations of lifting modules, Acta Math. Hungar., 91(3) (2001), 253-261.
[14] B. Kosar, C. Nebiyev and N. Sökmez, G-supplemented modules, Ukrainian Math. J., 67(6) (2015), 861-864.
[15] S. H. Mohamed and B. J. Müller, Continuous and discrete modules, London Math. Soc. Lecture Note Series, 147, Cambridge
University press, 1990.
[16] M. M. Obaid and T. Y. Ghawi, Principally g-supplemented modules, 9th International Scientific Conference of Iraqi Al-
Khwarizmi Society, 2022, to appear.
[17] A. C. Ozcan and A. Harmanci, Duo modules, Glasgow Math. J., 48(2006), 533-545.
[18] T. C. Quynh and P. H. Tin, Some properties of e-supplemented and e-lifting modules, Vietnam J. Math., 41(2013), 303-312.
[19] L. V. Thuyet and P. H. Tin, Some characterizations of modules via Essential small submodules, Kyungpook Math. J., 56(2016),
1069-1083.
[20] A. Tuganbaev, Semi distributive modules and rings, Kluwer Academics Publishers, Dordrecht, 1998.
[21] B. Ungor, S. Halicioglu and A. Harmanci, On a class of ⨁-supplemented modules, in Ring Theory and Its Applications,
Contemporary Mathematics, Amer. Math. Soc., 2014, 123–136.
[22] B. Ungor, S. Halicioglu and A. Harmanci, On a class of δ-supplemented modules, Bull. Malays. Math. Sci. Soc., 37(3)(2014),
703-717.
[23] G.V. Wilson, Modules with the summand intersection property, comm. In Algebra, 14(1986), 21-38.
[24] R. Wisbauer, Foundations of module and ring theory, University of Dusseldorf, 1991.
[25] R. Wisbauer, Modules and algebras: bimodule structure and group actions on algebras, Pitman Monographs and Surveys in Pure
and Applied Mathematics, 81, Longman, Harlow. MR1396313 (97i:16002), 1996.
[26] J. M. Zelmanowitz, Representation of rings with faithful polyform modules, Comm. Algebra, 14(1986), 1141-1169.
[27] Y. Zhou, Generalizations of perfect, semiperfect and semiregular rings, Algebra Colloq., 7(3)(2000), 305-318.
[28] D.X. Zhou and X.R. Zhang, Small-essential submodules and Morita Duality, Southeast Asian Bulletin of Mathematics, 35(2011),
1051-1062.
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Published
2022-04-22
How to Cite
Obaid, M. M., & Ghawi, T. Y. (2022). Principally ⨁-g-supplemented modules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(1), Math Page 24– 32. https://doi.org/10.29304/jqcm.2022.14.1.906
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