More on the dual notion of n-absorbing submodules
DOI:
https://doi.org/10.5269/bspm.66241Abstract
Let n be a positive integer. In this paper, the dual notion of n-absorbing submodules is studied in more detail from a functional point of view. Some related results and useful examples concerning this class of submodules are investigated. Also, we answer Question 2.5, in [6].
References
1. Anderson, D. F., Badawi, A., On n-absorbing ideals of commutative rings, Comm. Algebra 39, 1646-1672, (2011).
2. Anderson, D. D., Bataineh, M., Generalizations of prime ideals, Comm. Algebra 36, 686-696, (2008).
3. Ansari-Toroghy, H., Farshadifar, F., The dual notions of some generalizations of prime submodules, Comm. Algebra 39, 2396-2416, (2011).
4. Ansari-Toroghy, H., Farshadifar, F., On the dual notion of prime submodules, Algebra Colloq. 19(spec01), 1109-1116, (2012).
5. Ansari-Toroghy, H., Farshadifar, F., On the dual notion of prime submodules(II), Mediterr. J. Math. 9, 327-336, (2012).
6. Ansari-Toroghy, H., Farshadifar, F., Maleki-Roudposhti, S., N-absorbing and strongly n-absorbing second submodules, Bol. Soc. Parana. Mat. 39(1), 9-22, (2021).
7. Ansari-Toroghy, H., Farshadifar, F., The dual notion of multiplication modules, Taiwanese J. Math. 11(4), 1189-1201, (2007).
8. Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc. 75, 417-429, (2007).
9. Darani, A. Y., Soheilnia, F., On n-absorning submodules, Math. Commun. 17, 547-557, (2012).
10. Ebrahimpour, M., Nekooei, R., On generalizations of prime ideals, Comm. Algebra 40, 1268-1279, (2012).
11. Ebrahimpour, M., Nekooei, R., On generalizations of prime submodules, Bull. Iranian Math. Soc. 39(5), 919-939, (2013).
12. Ebrahimpour, M., On generalizations of prime ideals(II), Comm. Algebra 42, 3861-3875, (2014).
13. Gopalakrishnan, N. S., Commutative algebra. Oxonian Press Pvt. Ltd., New Delhi, (1984).
14. Hungerford, T. W., Algebra. Holt, Rinehart and Winston, New York, (1974).
15. Lu, C. P., Prime submodules of modules, Comment. Math. Univ. St. Pauli 33, 61-69, (1984).
16. Lu, C. P., Spectra of modules, Comm. Algebra 23, 3741-3752, (1995).
17. Marcelo, A., Masque, J., Prime submodules. the descent invariant and modules of finite length, J. Algebra 189, 273-293, (1997).
18. McCasland, R. L., Smith, P. F., Prime submodules of Noetherian modules, Rocky Mountain J. Math. 23, 1041-1062, (1993).
19. Tiras, Y., Tercan, A., Harmanci, A., Prime modules, Honam Math J. 18, 5-15, (1996).
20. Yasemi, S., The dual notion of prime submodules, Arch. Math. (Brono) 37(4), 273-278, (2001).
2. Anderson, D. D., Bataineh, M., Generalizations of prime ideals, Comm. Algebra 36, 686-696, (2008).
3. Ansari-Toroghy, H., Farshadifar, F., The dual notions of some generalizations of prime submodules, Comm. Algebra 39, 2396-2416, (2011).
4. Ansari-Toroghy, H., Farshadifar, F., On the dual notion of prime submodules, Algebra Colloq. 19(spec01), 1109-1116, (2012).
5. Ansari-Toroghy, H., Farshadifar, F., On the dual notion of prime submodules(II), Mediterr. J. Math. 9, 327-336, (2012).
6. Ansari-Toroghy, H., Farshadifar, F., Maleki-Roudposhti, S., N-absorbing and strongly n-absorbing second submodules, Bol. Soc. Parana. Mat. 39(1), 9-22, (2021).
7. Ansari-Toroghy, H., Farshadifar, F., The dual notion of multiplication modules, Taiwanese J. Math. 11(4), 1189-1201, (2007).
8. Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc. 75, 417-429, (2007).
9. Darani, A. Y., Soheilnia, F., On n-absorning submodules, Math. Commun. 17, 547-557, (2012).
10. Ebrahimpour, M., Nekooei, R., On generalizations of prime ideals, Comm. Algebra 40, 1268-1279, (2012).
11. Ebrahimpour, M., Nekooei, R., On generalizations of prime submodules, Bull. Iranian Math. Soc. 39(5), 919-939, (2013).
12. Ebrahimpour, M., On generalizations of prime ideals(II), Comm. Algebra 42, 3861-3875, (2014).
13. Gopalakrishnan, N. S., Commutative algebra. Oxonian Press Pvt. Ltd., New Delhi, (1984).
14. Hungerford, T. W., Algebra. Holt, Rinehart and Winston, New York, (1974).
15. Lu, C. P., Prime submodules of modules, Comment. Math. Univ. St. Pauli 33, 61-69, (1984).
16. Lu, C. P., Spectra of modules, Comm. Algebra 23, 3741-3752, (1995).
17. Marcelo, A., Masque, J., Prime submodules. the descent invariant and modules of finite length, J. Algebra 189, 273-293, (1997).
18. McCasland, R. L., Smith, P. F., Prime submodules of Noetherian modules, Rocky Mountain J. Math. 23, 1041-1062, (1993).
19. Tiras, Y., Tercan, A., Harmanci, A., Prime modules, Honam Math J. 18, 5-15, (1996).
20. Yasemi, S., The dual notion of prime submodules, Arch. Math. (Brono) 37(4), 273-278, (2001).
Downloads
Published
2025-09-17
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
How to Cite
Ranjbar Hamghavandi, F., & Ebrahimpour, M. (2025). More on the dual notion of n-absorbing submodules. Boletim Da Sociedade Paranaense De Matemática, 43, 1-11. https://doi.org/10.5269/bspm.66241
