Geodesic
$\sigma$-filters of commutative $BE$-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 121-134

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The concept of σ-filters is introduced in commutative BE-algebras and some properties of these classes of filters are studied. Some equivalent conditions are derived for every filter of a commutative BE-algebra to become a σ-filter. Some necessary and sufficient conditions are given for every regular filter of a commutative BE-algebra to become a σ-filter. A set of equivalent conditions is given for the class of all σ-filters of a commutative BE-algebra to become a sublattice to the lattice of all filters.
Keywords: commutative $BE$-algebra, dual annihilator filter, prime filter, $\sigma $-filter, regular filter, O-filter 
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Sambasiva Rao, M. $\sigma$-filters of commutative $BE$-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 121-134. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_1_a10/