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Radical of filters on hoops | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 7، بهمن و اسفند 2023، صفحه 127-143 اصل مقاله (230.36 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7661 | ||
| نویسندگان | ||
| R. A. Borzooei* 1؛ M. Aaly Kologani2؛ G. R. Rezaei3 | ||
| 1Shahid Beheshti University | ||
| 2Hatef Higher Education Institute, Zahedan, Iran | ||
| 3Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. | ||
| چکیده | ||
| In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology. | ||
| کلیدواژه‌ها | ||
| Hoop؛ maximal filter؛ prime filter؛ radical؛ r-filter؛ p-filter | ||
| مراجع | ||
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[2] M. Aaly Kologani, Y. B. Jun, R. A. Borzooei, Regular and Boolean elements in hoops and constructing Boolean algebras using regular filters, Analele stiintifice ale Universitatii Ovidius Constanta, 31(2) (2023), 5-22.
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[18] A. Paad, R. A. Borzooei, On semi-maximal filters on BL-algebras, Journal of Algebraic Systems, 6(2) (2019), 101-116.
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