University of Guilan Journal of Algebra and Related Topics 2345-3931 9 1 2021 06 01 $n$-fold obstinate and $n$-fold fantastic (pre)filters of $EQ$-algebras 31 50 4807 10.22124/jart.2021.16939.1210 EN A. Paad Department of Mathematics, University of Bojnord, Bojnord, Iran A. Jafari Department of Mathematics, University of Bojnord, Bojnord, Iran Journal Article 2020 06 28 In this paper, the notions of $n$-fold obstinate and $n$-fold fantastic (pre)filter<br />in $EQ$-algebras are introduced and the relationship among $n$-fold obstinate, maximal, $n$-fold fantastic, and $n$-fold (positive) implicative prefilters are investigated. Moreover, the quotient $EQ$-algebra induced by an $n$-fold obstinate filter is studied and it is proved that the quotient $EQ$-algebra induced by<br />an $n$-fold fantastic filter of a good $EQ$-algebra with bottom element $0$ is an involutive $EQ$-algebra. Finally, the relationships between types of $n$-fold filters in residuated $EQ$-algebras is shown by diagrams https://jart.guilan.ac.ir/article_4807_831eee65e67c44517d7e82c2e5f40330.pdf