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Extensions of Z−ideals in MV−algebras | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 21، شماره 4، مهر و آبان 2024، صفحه 23-34 اصل مقاله (427.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2024.48312.8498 | ||
| نویسندگان | ||
| A Hassani Movahed1؛ M Bedrood2؛ Arsham Borumand Saeid* 3 | ||
| 1Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132. 84084 Fisciano, SA, Italy. | ||
| 3Dept. of Math Shahid Bahonar University of Kerman | ||
| چکیده | ||
| In this paper, we introduce a special types of Z−ideals in MV −algebras and delve into their properties. These particular ideals are thoroughly examined within the context of MV −chains, semi-simple MV −algebras and Hyperarchimedean structures. Furthermore, we provide characterizations for these ideals, offering equivalent definitions that enhance our understanding of their nature. Our investigation also encompasses the relationships between these special Z−ideals and other types of ideals, such as the minimal prime ideals and the maximal ideals. Overall, this paper aims to provide a comprehensive analysis of special Z−ideals in MV −algebras. | ||
| کلیدواژهها | ||
| MV -algebra؛ ZJ−ideal؛ ZNJ−ideal | ||
| مراجع | ||
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[1] M. Bedrood, F. Sajadian, A. Borumand Saeid, Z◦−ideals in MV −algebras of continuous function, Filomat, 36(7) (2022), 2439-2450. https://doi.org/10.2298/FIL2207439B [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 (2023), 51-65. https://doi.org/10.36045/j.bbms.211109 [3] C. C. Chang, Algebraic analysis of many valued logic, Transactions of the AMS - American Mathematical Society, 88 (1958), 467-490. https://www.ams.org/journals/tran/1958-088-02/S0002-9947-1958-0094302-9/ S0002-9947-1958-0094302-9.pdf [4] R. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic foundations of many-valued reasoning, Kluwer Academic, Dordrecht, 2000. https://doi.org/10.1007/978-94-015-9480-6 [5] A. Filipoiu, G. Georgescu, A. Lettieri, Maximal MV −algebras, Mathware, Soft Computing, 4 (1997), 53-62. http: //eudml.org/doc/39098 [6] 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 [7] F. Forouzesh, F. Sajadian, M. Bedrood, Some results in types of extensions of MV −algebras, Publications de l’lnstitut Mathematique, 105(119) (2019), 161-177. https://doi.org/10.2298/PIM1919161F [8] C. S. Hoo, Maximal and essential ideals of MV −algebras, Mathware Soft Computing, 2 (1995), 181-196. https: //upcommons.upc.edu/bitstream/handle/2099/2471/hoo.pdf [9] A. Iorgulescu, Algebras of logic as BCK-algebras, Bucharest University of Economics Bucharest, Romania, 2008.
[10] A. H. Movahed, M. Bedrood, A. Borumand Saeid, On 2−absorbing ideals in MV −algebras, Submitted.
[11] D. Piciu, Algebras of fuzzy logic, Ed. Universitaria Craiova, 2007. | ||
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