N-FOLD OBSTINATE AND N-FOLD FANTASTIC (PRE)FILTERS OF EQ-ALGEBRAS

In this paper, the notions of n-fold obstinate and nfold fantastic (pre)filter 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 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.