Semi-Small Compressible Modules and Semi-Small Retractable Modules

Mohammed Baqer Hashim Al Hakeem; Nuhad S. Al-Mothafar; Maryam Haghjooyan

doi:10.30526/36.4.3156

Authors

Mohammed Baqer Hashim Al Hakeem Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq.
Nuhad S. Al-Mothafar Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq.
Maryam Haghjooyan Ministry of Education, Tazkiyeh High School, Motahari St. Darya St., Saadat Abad, Tehran, Iran.

DOI:

https://doi.org/10.30526/36.4.3156

Keywords:

compressible module, retractable module, small sub module, semi-small sub module, semi-small compressible module, semi-small retractable module.

Abstract

Let be a commutative ring with 1 and be left unitary . In this paper we introduced and studied concept of semi-small compressible module (a is said to be semi-small compressible module if can be embedded in every nonzero semi-small submodule of . Equivalently, is semi-small compressible module if there exists a monomorphism , , is said to be semi-small retractable module if , for every non-zero semi-small sub module in . Equivalently, is semi-small retractable if there exists a homomorphism whenever .

In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible and retractable respectively and give some of their advantages characterizations and examples.

References

Mohammed,B.H.ALhakeem.; Nuhad S. Al. Mothafar . P-small Compressible Modules and P-small Retractable Modules. Ibn Al-Haitham Journal for Pure and Applied Science, to appear.

Nuhad, S. Al-Mothafar.; Mohammed B. H. Alhakeem. Nearly Semiprime sub modules. Iraqi Journal of Science, 2015, 56, 4, 3210-3214.

Mijbass, A. S.; Nada Khalid Abdullah. semi-small sub modules. Tikrit Journal of Pure Science, 2011, 16, 1,104-107.

Israa. H. Muslem.; Some types Of Retractable and Compressible Modules. M.Sc.thesis. 2016. College of Education for pure Science. University of Baghdad.

Fluery, P.; Hollow modules and local endomorphism rings. Pacific J. Math. 1974.53. 379–385. DOI: https://doi.org/10.2140/pjm.1974.53.379

Diop.P.C.; Dia. M.L. On E-Small Compressible Modules. Journal of Algebra and Related Topics. 2021,9,2,69-81.

T. Y. Ghawi.; Some Generalization of Quasi-Dedekind Modules. M.Sc. Thesis , University of Baghdad, College of Education Ibn Al-Haitham, 2010.

Hadi, I. M., and Marhun, H. K. Small Monoform Modules. Ibn AL-Haitham Journal for Pure and Applied Sciences, 2017,27,2, 229–240.