TY - JOUR
ID - 42342
TI - Some Types of Filters in Equality Algebras
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Borzooei, Rajabali
AU - Zebardast, Fateme
AU - Aaly Kologani, Mona
AD - Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
AD - Department of Mathematics, Payam e Noor University, Tehran, Iran.
AD - Payam e Noor University
Y1 - 2017
PY - 2017
VL - 7
IS - Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
SP - 33
EP - 55
KW - Equality algebra
KW - (positive) implicative filter
KW - fantastic filter
KW - Boolean filter
DO -
N2 - Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras.
UR - https://cgasa.sbu.ac.ir/article_42342.html
L1 - https://cgasa.sbu.ac.ir/article_42342_cf5624efc3f4dd8d61c28cc7af659734.pdf
ER -