Noetherian, Artinian Regular Modules and Injective Property
DOI:
https://doi.org/10.29304/jqcm.2021.13.1.764Keywords:
Injective module, Regular module, Noetherian module, Artinian module, Cyclic moduleAbstract
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.
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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.
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[6] Fuchs, L., & Salce, L. (2001). Modules over non-Noetherian domains (No. 84). American Mathematical Soc.
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[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.
[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.
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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
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