On NM-Hollow Modules
DOI:
https://doi.org/10.29304/jqcm.2021.13.1.765Keywords:
Hollow module, Small submodule, Maximal submodule, Prime submodule, Finitely generated moduleAbstract
This notion investigates the generalization of hollow module namely near maximal hollow module (NM-hollow module). Any module M is NM-hollow if for every H satisfy two properties namely nearly and maximal. Some new results have been studied and more relationships are presented. The main result in this section is; if M is a faithful and multiplication over the ring R, then M is NM-hollow module. Also, a direct-sum of NM-hollow module is also NM-hollow.
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References
[1] Muna A. Ahmed, Nearly Maximal Submodules, Basrah Journal of Scienec (A) Vol.34(1), 1-6, 2016
[2] C.P.Lu, (1984), Prime submodules of modules, Commutative Mathematics, University. Spatula, 33, 61-69.
[3] Nuhad S. A., Adwia J.A., Nearly Prim Submodules, International J. of Advanced Scientific and Technical Research, 5(6), (2015), 166-173.
[4] Fleury, P., (1974), Hollow Modules and Local Endomorphism Rings, Pac.J.Math., 53, 379-385.
[5] Inaam M. A. Hadi and Riadh K. Ali, on almost maximal subs, J.college Education, No.1(2008),190-197.
[6] Kasch, F., (1982), Modules and rings. London: Academic Press.
(A) Vol.34(1), 1-6, 2016.
[7] Mustafa Alkan, (2003), Prime Modules and Submodules, COMMUNICATIONS IN ALGEBRA_Vol. 31, No. 11, pp. 5253–5261.
[8] Inaam M.A., Tha,ar Y. G., Small Quasi-Dedekind Modules, Journal of Al-Qadisiyah for Computer Science and Mathematics 3nd. Sinentific Conference 19-20, APRIL-2011 Vol 3 No.2 Year 2011.
[2] C.P.Lu, (1984), Prime submodules of modules, Commutative Mathematics, University. Spatula, 33, 61-69.
[3] Nuhad S. A., Adwia J.A., Nearly Prim Submodules, International J. of Advanced Scientific and Technical Research, 5(6), (2015), 166-173.
[4] Fleury, P., (1974), Hollow Modules and Local Endomorphism Rings, Pac.J.Math., 53, 379-385.
[5] Inaam M. A. Hadi and Riadh K. Ali, on almost maximal subs, J.college Education, No.1(2008),190-197.
[6] Kasch, F., (1982), Modules and rings. London: Academic Press.
(A) Vol.34(1), 1-6, 2016.
[7] Mustafa Alkan, (2003), Prime Modules and Submodules, COMMUNICATIONS IN ALGEBRA_Vol. 31, No. 11, pp. 5253–5261.
[8] Inaam M.A., Tha,ar Y. G., Small Quasi-Dedekind Modules, Journal of Al-Qadisiyah for Computer Science and Mathematics 3nd. Sinentific Conference 19-20, APRIL-2011 Vol 3 No.2 Year 2011.
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Published
2021-03-04
How to Cite
Hameed, F. N., & Kalaf, K. S. (2021). On NM-Hollow Modules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 168– 172. https://doi.org/10.29304/jqcm.2021.13.1.765
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Math Articles
