ON SEMI MAXIMAL FILTERS IN BL-ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| مقاله 3، دوره 6، شماره 2، فروردین 2019، صفحه 101-116 اصل مقاله (339.27 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2018.6130.1305 | ||
| نویسندگان | ||
| Akbar Paad1؛ R. A. Borzooei* 2 | ||
| 1Department of Mathematics, University of Bojnord, P.O.Box 9453155111, Bojnord, Iran. | ||
| 2Department of Mathematics, Shahid Beheshti University, P.O.Box 1983969411, Tehran, Iran | ||
| چکیده | ||
| In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G\"{o} del algebra. Specially, we prove that in a G\"{o}del algebra, any fantastic filter is a semi maximal filter and any semi maximal filter is an (n-fold) positive implicative filter. Also, in a $BL$-algebra, any semi maximal and implicative filter is a positive implicative filter. Finally, we give an answer to the open problem in [S. Motamed, L. Torkzadeh, A. Borumand Saeid and N. Mohtashamnia, Radical of filters in BL-algebras, Math. Log. Quart. 57, No. 2, (2011), 166-179 ]. | ||
| کلیدواژهها | ||
| (Semi simple)BL-algebra؛ G ̈odel algebra؛ semi maximal filter؛ radical of filter | ||
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آمار تعداد مشاهده مقاله: 688 تعداد دریافت فایل اصل مقاله: 888 |
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