SAS-Injective Modules
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1247Keywords:
Injective modules., Small injective modules., SAS-injective modules., Semiartinian small submoduleAbstract
We introduce and investigate SAS-injective modules as a generalization of small injectivity. A right module over a ring is said to be SAS- -injective (where is a right -module) if every right-homomorphism from a semiartinian small right submodule of into extends to . A module is said to be SAS-injective, if is SAS- -injective. Some characterizations and properties of SAS-injective modules are given. Some results on small injectivity are extended to SAS-injectivity.
Downloads
Download data is not yet available.
References
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules. New York: Springer-Verlag, (1974).
I. Amin, M. Yousif and N. Zeyada, “Soc-injective rings and modules,” Comm. Algebra, 33 (2005), pp. 4229-4250.
P. E. Bland, Rings and Their Modules. Berlin:Walter de Gruyter & Co., ( 2011).
F. Kasch, Modules and Rings. London: Academic Press, (1982).
P. A. Grillet, Abstract Algebra 2nd edition. New York: GTM 242, Springer, (2007).
T. Y. Lam, Lectures on Modules and Rings. New York: Springer-Verlag, (1999).
A. R. Mehdi, “On L-injective modules,” Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28(2) (2018), pp. 176–192.
A. R. Mehdi and D. T. Abd Al-Kadhim, “(ρ,m)-N-Injective Modules,” J. Phys.: Conf. Ser., 1234 012098 (2019).
A. R. Mehdi and A. S. Tayyah, “SS-Injective Modules and Rings,” Journal of AL-Qadisiyah for computer science and mathematics, 9(2) (2017), pp. 57-70.
L. V. Thuyet and T. C. Quynh, “On small injective rings and modules,” J. Algebra and Its Applications, 8 (2009), pp. 379-387.
A. A. Tuganbaev, “ Multiplication modules,” J. Mathematical Sciences, 123 (2004), pp.3839-3905.
R. Wisbauer, Foundations of Module and Ring Theory. London: Gordon and Breach, (1991).
Y. Xiang, “Principally small injective rings,” Kyungpook Math. J., 51(2011), pp. 177-185.
N. Zeyada, S. Hussein, and A. Amin, “Rad-injective and almost-injective modules and rings,” Algebra Colloquium, 18 (2011), pp.411-418.
I. Amin, M. Yousif and N. Zeyada, “Soc-injective rings and modules,” Comm. Algebra, 33 (2005), pp. 4229-4250.
P. E. Bland, Rings and Their Modules. Berlin:Walter de Gruyter & Co., ( 2011).
F. Kasch, Modules and Rings. London: Academic Press, (1982).
P. A. Grillet, Abstract Algebra 2nd edition. New York: GTM 242, Springer, (2007).
T. Y. Lam, Lectures on Modules and Rings. New York: Springer-Verlag, (1999).
A. R. Mehdi, “On L-injective modules,” Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28(2) (2018), pp. 176–192.
A. R. Mehdi and D. T. Abd Al-Kadhim, “(ρ,m)-N-Injective Modules,” J. Phys.: Conf. Ser., 1234 012098 (2019).
A. R. Mehdi and A. S. Tayyah, “SS-Injective Modules and Rings,” Journal of AL-Qadisiyah for computer science and mathematics, 9(2) (2017), pp. 57-70.
L. V. Thuyet and T. C. Quynh, “On small injective rings and modules,” J. Algebra and Its Applications, 8 (2009), pp. 379-387.
A. A. Tuganbaev, “ Multiplication modules,” J. Mathematical Sciences, 123 (2004), pp.3839-3905.
R. Wisbauer, Foundations of Module and Ring Theory. London: Gordon and Breach, (1991).
Y. Xiang, “Principally small injective rings,” Kyungpook Math. J., 51(2011), pp. 177-185.
N. Zeyada, S. Hussein, and A. Amin, “Rad-injective and almost-injective modules and rings,” Algebra Colloquium, 18 (2011), pp.411-418.
Downloads
Published
2023-09-25
How to Cite
Chyad, H. H., & Mehdi, A. R. (2023). SAS-Injective Modules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 31–40. https://doi.org/10.29304/jqcm.2023.15.2.1247
Issue
Section
Math Articles
