Noetherian, Artinian Regular Modules and Injective Property

Authors

  • Fawzi N. Hamad Department of Mathematics, University Of Anbar, Anbar, Iraq
  • Majid Mohammed Abed Department of Mathematics, University Of Anbar, Anbar, Iraq

DOI:

https://doi.org/10.29304/jqcm.2021.13.1.764

Keywords:

Injective module, Regular module, Noetherian module, Artinian module, Cyclic module

Abstract

   In this article we provide that several relationships between some concepts and injective module. We investigate, if  is a cyclic and regular module is injective. Also, if  is regular with N≤  is finitely generated submodule, so  is injective. Finally, some relationships have been studied about injective module in details.

Downloads

Download data is not yet available.

References

[1] Zelmanowitz J., (1972). Regular module, Transaction of the American mathematical society, Vol.163,.
[2] Funayama, N. (1966). Imbedding a regular ring in a regular ring with identity. Nagoya Mathematical Journal, 27(1), 61-64.‏
[3] Subhash Atal, (2014). Finitely generated Modules, M A498 project I, Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati-781039.
[4] Oshiro, K. (1984). Lifting modules, extending modules and their applications to QF-rings. Hokkaido Math. J, 13(3), 310-338.‏
[5] Lambek, J. (1966). Lectures on rings and modules, Blaisdell Publ. Com., Waltham, Toronto, London.‏
[6] Fuchs, L., & Salce, L. (2001). Modules over non-Noetherian domains (No. 84). American Mathematical Soc.
[7] Gilmer, R. (1992). Multiplicative ideal theory. Queen's Papers in Pure and Appl. Math., 90.‏
[8] Ware R., (1971). Endomorphism rings of projective Module, Trans. Amer. Math. Soc. 155,233-259.
[9] Inaam M.A., Tha,ar Y. G., Small Quasi-Dedekind Modules, Journal of Al-Qadisiyah for Computer Science and Mathematics 3nd. Sinentific Conference 19-20, APRIL-2011 Vol 3 No.2 Year 2011.

Downloads

Published

2021-03-04

How to Cite

Hamad, F. N., & Abed, M. M. (2021). Noetherian, Artinian Regular Modules and Injective Property. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 161– 167. https://doi.org/10.29304/jqcm.2021.13.1.764

Issue

Section

Math Articles