International Journal of Nonlinear Analysis and Applications
Essential-small fully stable modules
Document Type : Research Paper
Author
Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq
Abstract
We will add new types of modules over a ring $\mathfrak{R}$ called $\mathit{g}-$ small completely stable module and $\mathit{g}-$ small duo module, assuming $\mathfrak{R}$ is a ring with identity and $\mathcal{M}$ is a unitary left $\mathfrak{R}$-module. We also present the $\mathit{g}-$ small dual stable module, which is a duality. We show that our new ideas have characterization and a few properties.
Keywords
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[11] D. X. Zhou and X. R. Zhang, small-essential submodules and Morita duality, Southeast Asian Bull. Math. 35
(2011) 1051–1062.
[2] Z.A.EL. Bast and P.F. smith, Multiplication modules, Commun. Alg. 16 (1988) 755–779.
[3] J. F. Kasch Modules and Ring, Academic Press Inc. London, 1982.
[4] W. Khalid and A. S. Wadi, Generalized radical lifting modules, Int. J. Sci. Res. 10 (2017) 1383–1385.
[5] B. Kosar, C. Nebiyer and N. Sokmez, G-supplemented modules Ukrain. Math. ZJ. 6 (2015) 861–864.
[6] M.A. Inaam Hadi, e-hollow modules, In. J. Adv. Sci. Tech. Res. 3 (1997) 2249–9954.
[7] A. Ozcan, H. Harmanc and P.F. Smith, Duo modules, Glasgow Math. J. 48 (2006) 533–545.
[8] M. Tamer kosan, Generalized cofinitely semiperfect modules, Int. Elect. J. Alg. 5 (2009) 58–69.
[9] C. Vebiyev, G-Radical Supplemented Modules, Dep. Math. Ondokuz Mayıs University, 2016.
[10] R. Wisbauer, Foundations of Modules and Ring Theory, Gordonand Breach, Reading, 1991.
[11] D. X. Zhou and X. R. Zhang, small-essential submodules and Morita duality, Southeast Asian Bull. Math. 35
(2011) 1051–1062.
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Volume 12, Issue 2
November 2021Pages 1811-1816
- Receive Date: 26 March 2021
- Revise Date: 22 May 2021
- Accept Date: 13 July 2021