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S-spectral topology in MV -algebras | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 2، خرداد و تیر 2026، صفحه 65-80 اصل مقاله (468.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.52469.9254 | ||
| نویسندگان | ||
| fereshteh Forouzesh* 1؛ Mahta Bedrood2؛ Giacomo Lenzi2 | ||
| 1Higher Education Complex of Bam | ||
| 2Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132. 84084 Fisciano, SA, Italy. | ||
| چکیده | ||
| In this paper, we introduce new classes of ideals, called S-prime ideals and S-maximal ideals, based on a ∧-closed system S. The connection between these ideals and classical prime ideals is examined, and it is shown that every S-prime ideal constitutes a specific type of prime ideal. Moreover, it is proven that any proper ideal disjoint from S is contained in an S-prime ideal. The behavior of S-prime ideals is further analyzed in the setting of quotient MV -algebras, and their properties under isomorphisms are investigated. In the final part of the study, the complete ∧-closed system S is introduced, and a new topology, called the S-spectral topology, is defined using S and the family of S-ideals. Several topological properties of this space, including the Hausdorff, T0, and T1 separation axioms, are discussed. | ||
| کلیدواژهها | ||
| MV -algebra؛ ∧-closed system؛ S-prime ideal؛ S-spectral topology | ||
| مراجع | ||
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[1] 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 (2023), 51-65. https://doi.org/10.36045/j.bbms.211109 [2] M. Bedrood, F. Sajadian, G. Lenzi, A. Borumand Saeid, A generalization of prime ideals in MV-algebras, Journal of Algebra and Its Applications, 25(05) (2026). https://doi.org/10.1142/S0219498826500180 [3] 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 [4] C. C. Chang, Algebraic analysis of many-valued logic, Transactions of the American Mathematical Society, 88(2) (1958), 467-490. https://doi.org/10.2307/1993227 [5] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms, Transactions of the American Mathematical Society, 93(1) (1959), 74-80. https://doi.org/10.1090/S0002-9947-1959-0106489-0 [6] R. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic foundations of many-valued reasoning, Trends in Logic, Vol. 7, Kluwer Academic Publishers, Dordrecht, 2000. Reprinted by Springer Science & Business Media, 2013. https://doi.org/10.1007/978-94-015-9480-6 [7] A. Di Nola, F. Liguori, S. Sessa, Using maximal ideals in the classification of MV-algebras, Portugaliae Mathematica, 50(1) (1993), 87-102. [8] A. Filipoiu, G. Georgescu, A. Lettieri, Maximal MV-algebras, Mathware Soft Computing, 4(1) (1997), 53-62.
[9] F. Forouzesh, E. Eslami, A. Borumand Saeid, Spectral topology on MV-modules, New Mathematics and Natural Computation, 11(01) (2015), 13-33. https://doi.org/10.1142/S1793005715500027 [10] 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 [11] 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 [12] C. S. Hoo, MV-algebras, ideals and semisimplicity, Mathematica Japonica, 34(4) (1989), 563-583.
[13] C. S. Hoo, Molecules and linearly ordered ideals of MV-algebras, Publicacions Matem´atiques, 41(2) (1997), 455-465. https://www.jstor.org/stable/43737254 [14] A. Iorgulescu, J. B. Iorgulescu, Algebras of logic as BCK-algebras, Bucharest University of Economics, Bucharest, Romania, 2008. [15] M. Kolaˇr´ık, Independence of the axiomatic system for MV-algebras, Mathematica Slovaca, 63(1) (2013), 1-4. https://doi.org/10.2478/s12175-012-0076-z [16] 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 [17] 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 [18] 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 [19] D. Mundici, Advanced Lukasiewicz calculus and MV-algebras, Trends in Logic, Vol. 35, Springer, Berlin, 2011. https://doi.org/10.1007/978-94-007-0840-2 [20] J. R. Munkres, Topology, Dorling Kindersley, India, 2000.
[21] D. Piciu, Algebras of fuzzy logic, Ed. Universitaria Craiova, 2007. | ||
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