Modules with 2-Pure Intersection Property
Abstract
In this work, new concept is introduced and studied, which 2-pure submodule. Many results concerns with these concept are given.
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References
[1] Bahar H.Al-Bahranny, Modules with pure intersection properly , Ph.D. Thesis, University of Baghdad-Iraq,2000.
[2] Nuhad S.Al-Mathafar, Sums and Intersection of submodules, Ph.D. Thesis, University of Baghdad-Iraq,2002.
[3] Anderson F.W. and Fuller K.R., Rings and Categories of Modules, springer-vertag, Bertine, Heidelberg, New York, 1992.
[4] G.Desale, W.K.Nicholson,Endoprimite Rings,J. of algebra, v.70, pp 548-560, 1981.
[5] Sahra H. Yaseen , F-Regular Modules, M.Sc. Thesis University of Baghdad-Iraq,1993.
[6] Z.A. El-Bast and P.F. Smith, Multiplication Modules,Comm. Algebra, vol.16. pp.755-774, 1988.
[7] Faranak Farshadifar,n-Pure Submodules of Modules, Mathematics and Computational Science. Vol.5 No4, pp.48-53,Dec. 2024.
[8] Cohn, P.M, On the free product of associative rings, Mathematics Zeitschirft, vol.71,pp.380-398, 1959.
[9] Khaled Smiea Munshid, Mohamed Farhan Hamid, Jchad K., S-Pure submodules, vol.17 No.2, pp.917-922, 2022.
[10] Faranak Farshadifar , A generalization of Pure submodules, J. od algebra and related topics, vol.8 No.2,pp.1-8, Dec. 2020.
[11] Ali. S.Mijbass, Quasi-Dedekind Modules, Ph.D. Thesis, University of Baghdad-Iraq, 1997.
[12] M. S.Abbaas, On Fully stable Modules, Ph.D. Thesis, University of Baghdad, 1991.
[13] Ali, M.M., Smith, D.J, Pure submodules of multiplication Modules, Beitrage zur Algebra and Gemetric vol.45 No. 1, pp.61-74, 2004.
[14] Ansari-Toroghy, H., Faranak Farshifar, n-absorbing and strongly n-absorbing second submodules, Bol.Soc. Parana.Mat, vol.39, No1, pp.9-22, 2021.
[15] Ghaeb Ahmed Hammod, Generalization of Regular Modules and pure submodule, Ph.D.Thesis,University of Baghdad-Iraq, 2015.
[16] A.C.Özcan, A.Harmanci, Duo Modules, Glasgow Math.J.48 (2006) 533-545.
[17] Muna Abbas Ahmed, Iman Abulhadi Dhar , Zainab Abed Atiya, Purely Small Submodules and Purely Hollow Modules, Iraqi J. of Science vol.63 No.12,pp.5487-5495, 2022.
[18] Imed Kh. Salman and Nuhad S.Al-Mothafar, Almost Pure Ideals( submodules) and Almost Regular Rings(Modulezs) Iraqi J. of Science, vol.60 No.8, pp.1814-1819, 2019.
[19] Yusuf AlHoz,C-pure submodules and C-Flat Modules, J. of Universal Mathemartics, vol.4, No.2, pp. 222-229, 2021.
[20] Lam, T.Y., Lectures on Modules and Rings vol.189 springer series Business Media, 2012.
[2] Nuhad S.Al-Mathafar, Sums and Intersection of submodules, Ph.D. Thesis, University of Baghdad-Iraq,2002.
[3] Anderson F.W. and Fuller K.R., Rings and Categories of Modules, springer-vertag, Bertine, Heidelberg, New York, 1992.
[4] G.Desale, W.K.Nicholson,Endoprimite Rings,J. of algebra, v.70, pp 548-560, 1981.
[5] Sahra H. Yaseen , F-Regular Modules, M.Sc. Thesis University of Baghdad-Iraq,1993.
[6] Z.A. El-Bast and P.F. Smith, Multiplication Modules,Comm. Algebra, vol.16. pp.755-774, 1988.
[7] Faranak Farshadifar,n-Pure Submodules of Modules, Mathematics and Computational Science. Vol.5 No4, pp.48-53,Dec. 2024.
[8] Cohn, P.M, On the free product of associative rings, Mathematics Zeitschirft, vol.71,pp.380-398, 1959.
[9] Khaled Smiea Munshid, Mohamed Farhan Hamid, Jchad K., S-Pure submodules, vol.17 No.2, pp.917-922, 2022.
[10] Faranak Farshadifar , A generalization of Pure submodules, J. od algebra and related topics, vol.8 No.2,pp.1-8, Dec. 2020.
[11] Ali. S.Mijbass, Quasi-Dedekind Modules, Ph.D. Thesis, University of Baghdad-Iraq, 1997.
[12] M. S.Abbaas, On Fully stable Modules, Ph.D. Thesis, University of Baghdad, 1991.
[13] Ali, M.M., Smith, D.J, Pure submodules of multiplication Modules, Beitrage zur Algebra and Gemetric vol.45 No. 1, pp.61-74, 2004.
[14] Ansari-Toroghy, H., Faranak Farshifar, n-absorbing and strongly n-absorbing second submodules, Bol.Soc. Parana.Mat, vol.39, No1, pp.9-22, 2021.
[15] Ghaeb Ahmed Hammod, Generalization of Regular Modules and pure submodule, Ph.D.Thesis,University of Baghdad-Iraq, 2015.
[16] A.C.Özcan, A.Harmanci, Duo Modules, Glasgow Math.J.48 (2006) 533-545.
[17] Muna Abbas Ahmed, Iman Abulhadi Dhar , Zainab Abed Atiya, Purely Small Submodules and Purely Hollow Modules, Iraqi J. of Science vol.63 No.12,pp.5487-5495, 2022.
[18] Imed Kh. Salman and Nuhad S.Al-Mothafar, Almost Pure Ideals( submodules) and Almost Regular Rings(Modulezs) Iraqi J. of Science, vol.60 No.8, pp.1814-1819, 2019.
[19] Yusuf AlHoz,C-pure submodules and C-Flat Modules, J. of Universal Mathemartics, vol.4, No.2, pp. 222-229, 2021.
[20] Lam, T.Y., Lectures on Modules and Rings vol.189 springer series Business Media, 2012.
Published
2025-09-18
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