پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 838 |
| تعداد مقالات | 8,088 |
| تعداد مشاهده مقاله | 15,230,564 |
| تعداد دریافت فایل اصل مقاله | 10,171,849 |
On properties of closed sets in the Zariski topology of MV -algebras | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 3، مرداد و شهریور 2026، صفحه 15-29 اصل مقاله (449.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.9911 | ||
| نویسندگان | ||
| M. Bedrood1؛ R. A. Borzooei2، 3؛ G. Lenzi1؛ A. Borumand Saeid* 4، 5 | ||
| 1Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132. 84084 Fisciano, SA, Italy | ||
| 2Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran | ||
| 3Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye. | ||
| 4Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. | ||
| 5Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences (SIMATS) Chennai India. | ||
| چکیده | ||
| This paper presents a localized approach to the Zariski topology by restricting the spectral space to specific subsets of prime ideals within an MV -algebra. We investigate a particular class of Zariski-closed sets and demonstrate that they form a lattice under set inclusion. A distinguished filter within this lattice is then examined, and its algebraic properties are analyzed in detail. Building on this framework, we introduce the concept of vX-ideals, a new type of ideal defined in terms of these closed sets. We explore their algebraic behavior, including interactions with minimal prime ideals and their stability under homomorphisms. The study reveals new structural insights into Zariski-closed sets and their connections to broader ideal-theoretic constructs. The final diagram synthesizes these findings, offering a unified perspective and laying the foundation for further exploration of topological and algebraic properties in MV -algebras. | ||
| کلیدواژهها | ||
| MV -algebra؛ vX-ideal؛ lattice | ||
| مراجع | ||
|
[1] M. Bedrood, A. H. Movahed, G. Lenzi, A. Borumand Saeid, Study of MaxP-ideals and MinP -ideals in MV -algebras, submitted. [2] M. Bedrood, F. Sajadian, G. Lenzi, A. Borumand Saeid, Z◦-ideals and Z-ideals in MV -algebras, Bulletin of the Belgian Mathematical Society – Simon Stevin, 30(1) (2023), 51-65. https://doi.org/10.36045/j.bbms.211109 [3] M. Bedrood, F. Sajadian, G. Lenzi, A. Borumand Saeid, A generalization of prime ideals in MV-algebras, Journal of Algebra and its Applications, 25(5) (2026), 2650018. https://doi.org/10.1142/S0219498826500180 [4] L. P. Belluce, A. Di Nola, A. Lettieri, Local MV -algebras, Rendiconti del Circolo Matematico di Palermo, 42(2) (1993), 347-361. https://doi.org/10.1007/BF02844626 [5] L. P. Belluce, A. Di Nola, S. Sessa, The prime spectrum of an MV -algebra, Mathematical Logic Quarterly, 40(3) (1994), 331-346. https://doi.org/10.1002/malq.19940400304 [6] V. Cavaccini, C. Cella, G. Georgescu, Pure ideals of MV -algebras, Mathematica Japonica, 45(2) (1997), 303-310.
[7] C. C. Chang, Algebraic analysis of many valued logics, Transactions of the American Mathematical Society, 88 (1958), 467-490. https://doi.org/10.2307/1993227 [8] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms, Transactions of the American Mathematical Society, 93 (1959), 74-80. https://doi.org/10.2307/1993423 [9] R. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic foundations of many-valued reasoning, Kluwer Academic Publishers, Dordrecht, 2000. https://doi.org/10.1007/978-94-015-9480-6 [10] A. Di Nola, L. Leu¸stean, MV -algebras and Lukasiewicz logic, in Handbook of Mathematical Fuzzy Logic, Vol. 2 (2011), 469-583. [11] A. Di Nola, F. Liguori, S. Sessa, Using maximal ideals in the classification of MV -algebras, Portugaliae Mathematica, 50(1) (1993), 87-102. [12] A. Filipoiu, G. Georgescu, A. Lettieri, Maximal MV -algebras, Mathware and Soft Computing, 4 (1997), 53-62.
[13] F. Forouzesh, M. Bedrood, G. Lenzi, From Z◦-ideals to weak Z◦-ideals in MV -algebras, submitted.
[14] F. Forouzesh, E. Eslami, A. Borumand Saeid, On obstinate ideals in MV -algebras, Scientific Bulletin of Politehnica University of Bucharest, Series A, 76(2) (2014), 53-62. [15] F. Forouzesh, F. Sajadian, M. Bedrood, Inverse topology in MV -algebras, Mathematica Bohemica, 144(3) (2019), 273–285. https://doi.org/10.21136/MB.2018.0117-17 [16] F. Forouzesh, F. Sajadian, M. Bedrood, Some results in types of extensions of MV -algebras, Publications de l’Institut Math´ematique, 105(119) (2019), 161-177. https://doi.org/10.2298/PIM1919161F [17] C. S. Hoo, MV -algebras, ideals and semisimplicity, Mathematica Japonica, 34(4) (1989), 563-583.
[18] C. S. Hoo, Molecules and linearly ordered ideals of MV -algebras, Publicacions Matem`atiques, 41 (1997), 455-465.
[19] A. Iorgulescu, Algebras of logic as BCK-algebras, Bucharest University Press, 2008.
[20] A. H. Movahed, M. Bedrood, A. Borumand Saeid, Extensions of Z-ideals in MV -algebras, Iranian Journal of Fuzzy Systems, 21(4) (2024), 23-34. https://doi.org/10.22111/ijfs.2024.48312.8498 [21] A. H. Movahed, M. Bedrood, A. Borumand Saeid, On 2-absorbing ideals in MV -algebras, Filomat, 39(9) (2025), 2941-2951. https://doi.org/10.2298/FIL2509941M [22] A. H. Movahed, M. Bedrood, A. Borumand Saeid, Study of MV -algebras in view of R-ideals and 2R-ideals, Fuzzy Sets and Systems, 508 (2025), 109313. https://doi.org/10.1016/j.fss.2025.109313 [23] A. H. Movahed, M. Bedrood, A. Borumand Saeid, A generalization of Z◦-ideals in MV -algebras, Journal of Algebraic Hyperstructures and Logical Algebras, 6(1) (2025), 63-73. https://doi.org/10.61838/kman.jahla.6. 1.5 [24] D. Piciu, Algebras of fuzzy logic, Editura Universitaria, Craiova, 2007. | ||
|
آمار تعداد مشاهده مقاله: 13 تعداد دریافت فایل اصل مقاله: 18 |
||