جۆری توێژینه‌وه‌: Original Article

نوسه‌ران

Department of Mathematics, College of Science, University of Sulaimani, Sulaimani-Iraq.

پوخته‌

           In this paper, we focus on localization of certain types of submodules such as pure submodules, idempotent submodules, multiplication and multiplication submodules and we try to obtain some relations between these submodules and their localizations. Also, we prove that under certain conditions certain properties of modules can be transferred from the modules to their localizations and conversely at multiplicative systems that isolate these modules and also isolate the rings on which these modules are defined.

[1] Ali, M. M. and Smith, D. J.: Pure submodules of Multiplication Modules, Contributions to Algebra and Geometry, Vol. 45 (1) (2004), 61-74.

[2] Anderson, F. W. and Fuller, K. R.: Rings and categories of modules, springer-verlarge, 1974.

[3] Bothaynah N. S., Hatam Y. K. and Layla S. M.: Purely and Weakly Purely Cancellation Modules, American Journal of Mathematics and Statistics, Vol. 4 (4) (2014), 186-190.

[4] Darani, A. Y. : Almost Primal Ideals in Commutative Rings, Chiang Mai J. Sci. Vol. 38(2) (2011), 161-165.

[5] Jabbar, A. K. : A generalization of prime and weakly prime submodules, Pure Mathematical sciences, Vol. 2 (1), (2013), 1-11.

[6] Jahromi, L. H. and Khaksari, A. : Weakly Pure Submodules of Multiplication Modules, Journal of Mathematical Sciences: Advances and Applications, Vol. 6 ( 2), (2010), 215-218.

[7] Khakasari, A. : Weakly Pure Submodules of Multiplication Modules, International Journal of Algebra, Vol. 5 (5), (2011), 247-250.

[8] Larsen, M. D. and McCarthy, P. J.: Multiplicative theory of ideals, Academic Press, New York and London, 1971.

[9] Wisbauer, R.: Foundations of module and ring theory, Gordon and Breach Science Publishers, 1991.