Volume 19, Issue 2 (9-2024)
IJMSI 2024, 19(2): 13-39 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Jaradat M. The Zariski Topology on Cl.Spec_g(M) as a Spectral Space. IJMSI 2024; 19 (2) :13-39
URL: http://ijmsi.ir/article-1-1638-en.html
URL: http://ijmsi.ir/article-1-1638-en.html
Abstract:
Let G be a group, R be a G-graded commutative ring with identity, M be a unitary graded R-module, Specg(R) be the set of graded prime ideals of R, and Cl.Specg(M) be the set of all graded classical prime submodules of M. In this paper among other things, the author studied the Zariski topology on both and Cl.Specg(M), and investigate some properties of the Zariski topology on Cl.Specg(M) and some conditions under which the graded classical prime spectrum of M is a spectral for its Zariski topology.
Type of Study: Research paper |
Subject:
General
References
1. A. Abbasi, D. Hassanzadeh-Lelekaami, Modules and Spertral Space, Comm. Algebra, 40, (2012), 4111-4129. [DOI:10.1080/00927872.2011.602273]
2. A. Abbsi, D. Hassanzadeh-Lelekaami, Quasi-Prime Submodules and Developed Zariski Topology, Algebra Colloq., 19, (2012), 1089-1108. [DOI:10.1142/S1005386712000879]
3. R. Abu-Dawwas, K. Al-Zoubi, On Graded Weakly Classical Prime Submodules, Iran. J. Math. Sci. Inform., 12(1), (2017), 153-161. [DOI:10.1109/MACISE.2019.00007]
4. K. Al-Zoubi, R. Abu-Dawwas, On Graded Quasi-Prime Submodules, Kyungpook Math. J., 55(2), (2015), 259-266. [DOI:10.5666/KMJ.2015.55.2.259]
5. K. Al-Zoubi, M. Al-Dolat, On Graded Classical Primary Submodules, Adv. Pure Appl. Math., 7(2), ( 2016), 93-96. [DOI:10.1515/apam-2015-0021]
6. K. Al-Zoubi, M. Jaradat, On the Graded Classical Prime Spectrum of a Graded Module, Proyeccions Journal of Mathematics, 37(3), (2018), 519-533. [DOI:10.4067/S0716-09172018000300519]
7. K. Al-Zoubi, M. Jaradat, The Zariski Topology on the Graded Classical Prime of a Graded Module Over a Graded Commutative Ring, Matematicki Vesnik, 70(4), (2018), 303-313.
8. K. Al-ZoubiI, M. Jaradat, R. Abu-Dawwas, On Graded Classical Prime and Graded Prime Submodules, Bull. Iranian Math. Soc., 41(1), (2015), 217-225.
9. H. Ansari-Toroghy, R. Ovlyaee-Sarmazdh, On the Prime Spectrum of a Module and Zariski Topologies. Comm. Algebra, 38, (2010), 4461-4475. [DOI:10.1080/00927870903386510]
10. H. Ansari-Toroghy, S. S. Pourmortazavi, On the Prime Spectrum of Modules, Miskolc Math Notes, 16(2), (2015), 1233-1242. [DOI:10.18514/MMN.2015.1102]
11. S. E. Atani, On Graded Prime Submodule, Chiang Mai. J. Sci., 33(1), (2006), 3-7.
12. S. E. Atani, F. Farzalipour, Notes on the Graded Prime Submodules, International Mathematical Forum, 38(1), (2006), 1871-1880. [DOI:10.12988/imf.2006.06162]
13. S. E. Atani, F. E. K. Saraei, Graded Modules Which Satisfy The Gr-Radical formula, Thai J. Math., 8(1), (2010), 161-170.
14. M. F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Longman Higher Education, New York, 1969.
15. M. Behboodi, M. R. Haddadi, Classical Zariski Topology of Modules and Spectral Spaces I, International Electrontc Journal Of Algebra, 4(4), (2008), 104-130.
16. M. Behboodi, M. R. Haddadi, Classical Zariski Topology of Modules and Spectral Spaces II, International Electrontc Journal of Algebra, 4(4), (2008), 131-148.
17. N. Bourbaki, Algebra Commutative, Hermann, Paris, 1961.
18. A. Y. Darani, Topology on Specg(M), Bul Acad. Stiinte Repub Mold. Mate., 3(67), (2011), 45-53.
19. A. Y. Darani, S. Motmaen, Zariski Topology on the Spectrum of Graded Classicl Prime Submodules, Appl. Gen Topol., 14(2), (2013), 159-169. [DOI:10.4995/agt.2013.1586]
20. T. Duralvel, Topology On Spectrume of Module, J. Ramanujan Math. Soc., 9(1), (1994), 25-34.
21. R. Hazrat, Graded Rings and Graded Grothendieck Groups, Cambridge University Press, Cambridge, 2016. [DOI:10.1017/CBO9781316717134]
22. M. Hochster, Prime Ideal Structure in Commutative Rings, Trans. Amer. Math. Soc, 137, (1969), 43-60. [DOI:10.1090/S0002-9947-1969-0251026-X]
23. M. Jesper. Moller, General Topology, Matematisk Institut, Universite tsparken 5, DK-2100 Kobenhavn.
24. E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry. Boston: Birkh¨auser., 1985. [DOI:10.1007/978-1-4612-5290-0]
25. S. C. Lee, R. Varmazyar, Semiprime Submodules of Graded Multiplication Modules, J. Korean Math. Soc., 49(2), (2012), 435-447. [DOI:10.4134/JKMS.2012.49.2.435]
26. C. P. Lu, Modules With Noetherian Spertrum, Comm. Algebra, 38(3), (2010), 807-828. [DOI:10.1080/00927870802578050]
27. C. P. Lu, The Zariski Topology On the Prime Spectrum of a Module., Houston J. Math, 25(3), (1999), 417-432.
28. J. R. Munkres, Topology; A first Course, Prentice-Hall, Inc, Eaglewood Cliffs, New Jersey, 1975.
29. R. L. McCasland, M. E. Moore, t. P Smith, On the Spectrum Over a Commutative Ring, Comm. Algebra, 25, (1997), 79-103. [DOI:10.1080/00927879708825840]
30. C. Nastasescu, F. Van Oystaeyen, Graded Ring Theory, Mathematical Library 28, NorthHolland, Amsterdam, 1982.
31. C. Nastasescu, V. F. Oystaeyen, Methods of Graded Rings, LNM 1836. Berlin-Heidelberg: Springer-Verlag, 2004. [DOI:10.1007/b94904]
32. K. H. Oral, U. Tekir, A. G. Agargun, On Graded Prime and Primary Submodules, Turk J. Math, 1(35), (2011), 159-167.
33. R. Ovlyaee-Sarmazdh, S. Maleki-Roudposhti, On Max-Injective Modules, Journal Of Algebra And Related Topics., 1(1), (2013), 57-66.
34. N. A. Ozkirisci, K. H. Oral and U. Tekir, Graded Prime Spectrum of a Graded, Iranian Journal Of Science and Technology, 4(4), (2013), 411-420.
35. M. Refai, On Properties of G-Spec(R), Sci. Math. Jpn., 4, (2001), 491-495.
36. M. Refai, K. Al-Zoubi, On Graded Primary Ideals, Turk. J. Math., 28, (2004), 217-229.
37. M. Refai, M. Hailat, S. Obiedat, Graded Radical on Graded Prime Spectra, Far East J. of Math. Sci., part I, (2000), 59-73.
38. R. N. Uregen, U. Tekir, K. H. Oral, On the :union: of Graded Prime Ideals, Open Phys., 14, (2016), 114-118. [DOI:10.1515/phys-2016-0011]
39. H. A.Tavallaee, M. Zolfaghari, Graded Weakly Semiprime Submodules of Graded Multiplication Modules, Lobachevskii J. Math., 34(1), (2013), 61-67. [DOI:10.1134/S1995080213010113]
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
