Integral prefilters and integral Eq-algebras
Akbar Paad · Mathematica Slovaca · 2022
Abstract In this paper, the notion of some new classes of EQ-algebras which are called integral, O-local, and locally finite EQ-algebras are introduced, and relationships between locally finite EQ-algebras and maximal prefilters are described. Also, the notion of integral prefilters are introduced and several characteristics of them are presented. Moreover, relation among integral prefilters and some type of other prefilter such as positive implicative, maximal, prime, and fantastic prefilters in EQ-algebras are studied. Finally, Boolean prefilters in bounded lattice EQ-algebras are introduced, and it is proved that a filter of a prelinear involutive EQ-algebra L is a Boolean filter if and only if L/F is a Boolean algebra.