Strongly Uniform Extending Modules

Authors

  • Saad Abdulkadhim Al-Saadi Mustansiriyah university college science mathematics department
  • darya jabar abdulkareem Mustansiriyah university college science mathematics department

DOI:

https://doi.org/10.23851/mjs.v29i2.237

Keywords:

strongly uniform extending, strongly uniform continuous, strongly uniform quasi-continuous

Abstract

In this paper, we introduced and studied the concept of strongly uniform extending modules, An R-module M is called strongly uniform extending (or M has (1-SC1) condition) if every uniform submodule of M is essential in a stable (fully invariant) direct summand of M. As a proper stronger than uniform extending modules and as a generalization of strongly extending modules and give some properties of such modules in analogy with properties for strongly extending modules. We have the following implications: Strongly extending modules ⇒ Strongly uniform extending modules ⇒ Uniform extending modules.

Author Biographies

Saad Abdulkadhim Al-Saadi, Mustansiriyah university college science mathematics department

mathematics

darya jabar abdulkareem, Mustansiriyah university college science mathematics department

Mathematics

References

M.S.Abbas: On fully stable modules, Ph.D. Thesis, Univ. of Baghdad, 1991.

S.A.AL-Saadi: S-extending modules and related concepts, Ph. D. Thesis, Univ. of Mustansiriya, 2007.

M.A.EL-Baroudy: Modules in which complements are summands, Ph. D. Thesis, Uinv McMaster, 1986.

M.H.Ebrahiam El-Baroudy: On Generalization of continuous modules, M. Sc. Thesis, Univ of Ain Shams, 1991.

K.R.Goodearl: Ring theory: Non-singular rings and modules, Marcel Dekker, INC. New York and Basel (1976).

I.M.A.Hadi, R.N.Majeed: Min(Max)-CS Modules, Ibn AL- Haitham Journal for pure and Applied Science, 1(25) (2012), 408-420.

F.Kasch: Modules and rings, Academic Press. London, 1982 .

J.Lambek: Lectures on rings and modules, Chesea. Pub. Co., New York, 1976., New York,(1998).

S.H.Mohamed and B.J.Muller: Continuous and Discrete modules, London Math. Soc., LN 147, Cambridge, Univ. Press 1990. .

T.C.Quynh: Some characterization of ef-extending rings,Electronic J. Alge., 5(2009), 17-26. [11] P.F.Simth and A.Tercan: Continuous and quasi-continuous modules, Houston Math. J 18(1992), 339-348.

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Published

2018-11-17

How to Cite

[1]
S. A. Al-Saadi and darya jabar abdulkareem, “Strongly Uniform Extending Modules”, MJS, vol. 29, no. 2, pp. 148–154, Nov. 2018.

Issue

Section

Mathematics