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Abstract
of the concept of prime ideal. In this paper, we completely determine all S-prime and S-maximal ideals
of a principal domain. It is shown that the intersection of any descending chain of S-prime ideals in a
principal domain is an S-prime ideal, also the S-radical is investigated.
Keywords
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References
- Anderson, D. D., A note on minimal prime ideals, Proceedings of the AMS. Vol. 122 (1), 1994.
- Anderson, D.D., Dumitrescu, T.: S-Noetherian rings. Commun. Algebr. 30, 44074416 (2002).
- Atiyah, M., McDonald, I. G. (2018). Introduction to Commutative Algebra. Oxford: Addison-Wesley Publishing Company.
- Eda Yldz, Bayram Ali Ersoy, nsal Tekir and Suat Ko (2020): On S-Zariski topology, Communications in Algebra
- Hamed, A., and Malek, A. (2019). S-prime ideals of a commutative ring. Beitrge Zur Algebra Und Geometrie.
- Hochster, M. (1971). The minimal prime spectrum of a commutative ring. Can. J. Math. 23(5):749758. DOI:10.4153/CJM-1971-083-8.
- Lim, J.W.: A note on S-Noetherian domains. Kyungpook Math. J.55, 507514 (2015)
- Liu, Z., On S-Noetherian rings. Arch. Math. (Brno) 43, 5560 (2007)
- McCoy, N.H., Rings and ideals. Carus Math. Monogr. 8, 96107 (1948)
- Ohm, J., Pendleton, R., Rings with Noetherian spectrum. Duke Math. J. 35:631639, (1968).
- Sevim, E. S., Arabaci, T., Tekir, U., Ko, S. (2019). ˙ On S-prime submodules. Turk. J. Math. 43(2):10361046.
- Thomas W. Hungerford. On the structure of principal ideal rings. Pacific J. of math., Vol. 25, No. 3, 1968
- Wiegand, R., Wiegand, S. Prime ideals in Noetherian rings. Surv. Trend. Math. 13, 175193 (2010)
- Wiegand, S., Intersections of prime ideals in Noetherian rings. Comm. Algebr. 11, 18531873 (1983)
- O. Zariski and P. Samuel, Commutative Algebra, volume I, Van Nostrand, Princeton, 1960
References
Anderson, D. D., A note on minimal prime ideals, Proceedings of the AMS. Vol. 122 (1), 1994.
Anderson, D.D., Dumitrescu, T.: S-Noetherian rings. Commun. Algebr. 30, 44074416 (2002).
Atiyah, M., McDonald, I. G. (2018). Introduction to Commutative Algebra. Oxford: Addison-Wesley Publishing Company.
Eda Yldz, Bayram Ali Ersoy, nsal Tekir and Suat Ko (2020): On S-Zariski topology, Communications in Algebra
Hamed, A., and Malek, A. (2019). S-prime ideals of a commutative ring. Beitrge Zur Algebra Und Geometrie.
Hochster, M. (1971). The minimal prime spectrum of a commutative ring. Can. J. Math. 23(5):749758. DOI:10.4153/CJM-1971-083-8.
Lim, J.W.: A note on S-Noetherian domains. Kyungpook Math. J.55, 507514 (2015)
Liu, Z., On S-Noetherian rings. Arch. Math. (Brno) 43, 5560 (2007)
McCoy, N.H., Rings and ideals. Carus Math. Monogr. 8, 96107 (1948)
Ohm, J., Pendleton, R., Rings with Noetherian spectrum. Duke Math. J. 35:631639, (1968).
Sevim, E. S., Arabaci, T., Tekir, U., Ko, S. (2019). ˙ On S-prime submodules. Turk. J. Math. 43(2):10361046.
Thomas W. Hungerford. On the structure of principal ideal rings. Pacific J. of math., Vol. 25, No. 3, 1968
Wiegand, R., Wiegand, S. Prime ideals in Noetherian rings. Surv. Trend. Math. 13, 175193 (2010)
Wiegand, S., Intersections of prime ideals in Noetherian rings. Comm. Algebr. 11, 18531873 (1983)
O. Zariski and P. Samuel, Commutative Algebra, volume I, Van Nostrand, Princeton, 1960