Some results on Stonean filters in equality algebras
نویسندگان
1 Department of Mathematics, Graduate University of Technology University, Kerman, Iran
2 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
3 Department of Mathematics, Graduate University of Technology University, Kerman, Iran
doi
10.22111/ijfs.2025.9268چکیده
The present paper aims to study the notion of Stonean filters on equality algebras and discusses the connection betweenthese filters and other types of filters on equality algebras. We show that any implicative filter, positive implicative filterand Boolean filter is a Stonean filter on equality algebras and by some counterexample, we show that the vice versa donot 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 theimplicative, positive implicative, Boolean and Stonean filters are equivalent together under the condition involutive onan 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 provideseveral examples to make the definitions clearer.
