More on the dual notion of n-absorbing submodules

Fatemeh Ranjbar Hamghavandi; Mahdieh Ebrahimpour

doi:10.5269/bspm.66241

Fatemeh Ranjbar Hamghavandi Vali-e-Asr University of Rafsanjan https://orcid.org/0000-0002-1338-0925
Mahdieh Ebrahimpour Vali-e-Asr University of Rafsanjan

Abstract

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].

Downloads

Download data is not yet available.

References

Anderson, D. F., Badawi, A., On n-absorbing ideals of commutative rings, Comm. Algebra 39, 1646-1672, (2011).

Anderson, D. D., Bataineh, M., Generalizations of prime ideals, Comm. Algebra 36, 686-696, (2008).

Ansari-Toroghy, H., Farshadifar, F., The dual notions of some generalizations of prime submodules, Comm. Algebra 39, 2396-2416, (2011).

Ansari-Toroghy, H., Farshadifar, F., On the dual notion of prime submodules, Algebra Colloq. 19(spec01), 1109-1116, (2012).

Ansari-Toroghy, H., Farshadifar, F., On the dual notion of prime submodules(II), Mediterr. J. Math. 9, 327-336, (2012).

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).

Ansari-Toroghy, H., Farshadifar, F., The dual notion of multiplication modules, Taiwanese J. Math. 11(4), 1189-1201, (2007).

Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc. 75, 417-429, (2007).

Darani, A. Y., Soheilnia, F., On n-absorning submodules, Math. Commun. 17, 547-557, (2012).

Ebrahimpour, M., Nekooei, R., On generalizations of prime ideals, Comm. Algebra 40, 1268-1279, (2012).

Ebrahimpour, M., Nekooei, R., On generalizations of prime submodules, Bull. Iranian Math. Soc. 39(5), 919-939, (2013).

Ebrahimpour, M., On generalizations of prime ideals(II), Comm. Algebra 42, 3861-3875, (2014).

Gopalakrishnan, N. S., Commutative algebra. Oxonian Press Pvt. Ltd., New Delhi, (1984).

Hungerford, T. W., Algebra. Holt, Rinehart and Winston, New York, (1974).

Lu, C. P., Prime submodules of modules, Comment. Math. Univ. St. Pauli 33, 61-69, (1984).

Lu, C. P., Spectra of modules, Comm. Algebra 23, 3741-3752, (1995).

Marcelo, A., Masque, J., Prime submodules. the descent invariant and modules of finite length, J. Algebra 189, 273-293, (1997).

McCasland, R. L., Smith, P. F., Prime submodules of Noetherian modules, Rocky Mountain J. Math. 23, 1041-1062, (1993).

Tiras, Y., Tercan, A., Harmanci, A., Prime modules, Honam Math J. 18, 5-15, (1996).

Yasemi, S., The dual notion of prime submodules, Arch. Math. (Brono) 37(4), 273-278, (2001).