Geodesic
New Kinds of Prefilters in EQ-Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 31-49

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In this paper, the notions of n-fold positive implicative prefilter and n-fold implicative prefilter in EQ-algebras are introduced and several properties, characterizations and equivalent conditions are provided. It is proved that the quotient EQ-algebra induced by an n-fold positive implicative prefilter is n-idempotent. Also, it is proved that in an n-idempotent EQ-algebra, any filter is an n-fold positive implicative filter. In the sequel, we investigate the relationships between these two types of prefilters. Finally, some characterizations of n-fold implicative prefilters in bounded EQ-algebras are given.
Keywords: (n-idempotent) EQ-algebra, n-fold positive implicative prefilter, n-fold implicative prefilter 
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Paad, Akbar; Bakhshi, Mahmood; Jafari, Azam; Rahimi, Maryam. New Kinds of Prefilters in EQ-Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 31-49. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a2/