جۆری توێژینه‌وه‌ : Original Article

نوسه‌ران

1 Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Iraq

2 Department of Mathematics, College of Education, University of Garmian, Garmian, Iraq

پوخته‌

In this paper Artinian and locally prime modules are studied and some
characterizations of locally prime modules are given. Some conditions are given
under which locally prime modules are almost prime modules and a nonzero
module is a locally prime module. Some properties of Artinian and locally Artinian
modules are given. Also, strongly reduced modules, primally reduced modules,
radically reduced modules and some other types are studied and investigated and
some properties of these types of modules are proved. In addition, some relations
that concerning these types of modules are established and some characterizations
of them are given.

وشه‌ بنچینه‌ییه‌كان

 
[1] Atani, S. E. and Darani, A. Y. : Notes on the Primal Submodules, Chiang Mai J. Sci.
35(3), 2008, pp 399-410.
[2] Atani, S. E. and Farzalipour, F. : On Weakly Prime Submodules, Tamkang Journal of Mathematics, Vol. 38, No. 3, 2007, 247-252.
[3] Azizi, A.: Prime Submodules of Artinian Modules, Taiwaness Journal of Mathematics, Vol. 13, No. 6B, pp. 2011-2020, 2009.
[4] Behboodi, M. , Karamzadeh, O.A.S. and Koohy, H. : Modules Whose Certain Submodules Are Prime, Vietnam Journal of Mathematics 32:3 (2004) pp 303-307.
[5] Jabbar, A. K.: A Generalization of Reduced Modules, International Journal of Algebra , Vol. 8, 2014, no. 1, 39-45.
[6] Jabbar, A. K.: On Locally Reduced and Locally Multiplication  Modules,  International Mathematical Forum, Vol. 8, 2013, no. 18, 851-858,
[7] Jabbar, A. K.: A Generalization of prime and weakly prime submodules, Pure Mathematical Sciences, Vol. 2,  2013, No. 1, 1-11 , 
[8] Jabbar, A. K.: On Locally Artinian Modules, International Journal of Algebra, Vol. 6, 2012, No. 27, 1325-1334.
[9] Jabbar, A. K. and Mohammad R. R.: The Effect of Localization on Properties of Certain Types of Modules, The 2nd International conference of the college of Education – University of Garmian held on 21-22/8/2016.
[10] Larsen, M. D. and McCarthy, P. J.: Multiplicative Theory of Ideals, Academic Press, New York and London, 1971.
[11] Lomp, C. and Pena, P. A. J. : A Note on Prime Modules, Divulgaciones Mathematicas, Vol. 8, No. 1, 2000, pp 31-42.
[12] Rajaee, S. : Comaximal Submodules of Multiplication Modules, International Mathematical Forum, Vol.5, 2010, no. 24, 1179-1183.