Characterizations of Weakly Approximately Primary Submodules in Some Types of Modules

Main Article Content

Khaled Y. Jhad
Bothaynah N. Shahab

Abstract

Our aim in this note is to introduce several characterizations of weakly approximately primary submodules in class of multiplication modules. Furthermore, we characterized weakly approximately primary submodules by theirs resudule in the class of multiplication modules with the help of some types of modules as non-singular, projective, regular and faithful modules. Also, we characterized weakly approximately primary ideal with some kind of weakly approximately primary submodules in the same previous classes of modules with help of finitely generated modules.

Article Details

How to Cite
Khaled Y. Jhad, & Bothaynah N. Shahab. (2021). Characterizations of Weakly Approximately Primary Submodules in Some Types of Modules. Tikrit Journal of Pure Science, 26(4), 85–90. https://doi.org/10.25130/tjps.v26i4.167
Section
Articles

References

[1] Khaled Y.J. and Bothaynah N.S. (2021), “Weakly Approximately Primary Submodule and Related concepts”, Tikrit Journal of Pure Sci to appear.

[2] Goodearl K.(1976), “Ring Theory”, Marcel Dekker, Inc. New york and Basel.

[3] Barnard A., (1981). “Multiplication Modules” Journal of Algebra, vol.(71), pp.(174-178).

[4] Darani A.Y. and Soheilnia F.(2011), “2-Absorbing and Weakly 2-Absorbing Submodules”, Tahi Journal of Math. , vol.(9), No.(3), pp.(577 -584).

[5] Naderi M. and Raza J.(2009), “Weakly Primary Submodules of Multiplication Modules and Intersection Theorem”, Int. Journal contemp, Math. Sci. vol.(4), No.(33), pp.(1645 -1652).

[6] Nuha H.H.(1996), “The Radicals of Modules”, M.s.c Thesis. University of Baghdad.

[7] Kash F. (1982) “Modules and Rings”, London Math. Soc. Morogrophs, New york Academic press.

[8] Mijbass A.S.(1993), “On Cancellation Modules” M.s.c Thesis. University of Baghdad.

[9] Sharp D. and Vamos P.(1972), “Injective Modules”Cambridge University press.