$n$-fold obstinate and $n$-fold fantastic (pre)filters of $EQ$-algebras

$n$ -fold obstinate and $n$ -fold fantastic (pre)filters of $E Q$ -algebras

Document Type : Research Paper

Authors

Department of Mathematics, University of Bojnord, Bojnord, Iran

Abstract

In this paper, the notions of

n

-fold obstinate and

n

-fold fantastic (pre)filter
in

E Q

-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

E Q

-algebra induced by an

n

-fold obstinate filter is studied and it is proved that the quotient

E Q

-algebra induced by
an

n

-fold fantastic filter of a good

E Q

-algebra with bottom element

0

is an involutive

E Q

-algebra. Finally, the relationships between types of

n

-fold filters in residuated

E Q

-algebras is shown by diagrams

Keywords