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Some results on Stonean filters in equality algebras | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 22، شماره 3، مرداد و شهریور 2025، صفحه 125-138 اصل مقاله (422.6 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2025.9268 | ||
| نویسندگان | ||
| M. Hadinejad1؛ M. M. Zahedi* 1؛ A. Borumand Saeid2 | ||
| 1Department of Mathematics, Graduate University of Technology University, Kerman, Iran | ||
| 2Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| The present paper aims to study the notion of Stonean filters on equality algebras and discusses the connection between these filters and other types of filters on equality algebras. We show that any implicative filter, positive implicative filter and Boolean filter is a Stonean filter on equality algebras and by some counterexample, we show that the vice versa do not generally hold. In addition, it is checked that the relations of Stonean filter with implicative filter, fantastic filter, Boolean filter, prime filter, maximal filter, ultra filter and positive implicative filter on equality algebras, while the implicative, positive implicative, Boolean and Stonean filters are equivalent together under the condition involutive on an equality algebra. The concept of primary filter is introduced, and its relationship with the prime filter is investigated. Finally, Stonean radical filter (Rads(F)) is introduced according to the concept of Stonean filter on equality algebras, and we prove that under a suitable condition if F is a prime filter, then Rads(F) = F. Also, in this article, we provide several examples to make the definitions clearer. | ||
| کلیدواژه‌ها | ||
| Equality algebra؛ (Stonean؛ implicative؛ fantastic؛ Boolean؛ prime؛ maximal؛ primary؛ Stonean radical) filter | ||
| مراجع | ||
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