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/

[1] S.S. Ahn, Y.H. Kim and J.M. Ko, Filters in commutative $BE$-algebras, Commun. Korean. Math. Soc. 27 (2) (2012) 233–242. https://doi.org/10.4134/CKMS.2012.27.2.233

[2] A. Borumand Saeid, A. Rezaei and R.A. Borzooei, Some types of filters in $BE$-algebras, Math. Comput. Sci. 7 (2013) 341–352. https://doi.org/10.1007/s11786-013-0157-6

[3] W.H. Cornish, O-ideals, congruences, sheaf representation of distributive lattices, Rev. Roum. Math. Pures et Appl. 22 (8) (1977) 1059–1067.

[4] K. Iseki and S. Tanaka, An introduction to the theory of $BCK$-algebras, Math. Japon. 23 (1) (1979) 1–6.

[5] H.S. Kim and Y.H. Kim, On $BE$-algebras, Sci. Math. Jpn. 66 (1) (2007) 113–116.

[6] B.L. Meng, On filters in $BE$-algebras, Sci. Math. Japon. (2010) 105–111. https://doi.org/10.32219/isms.71.2-201

[7] S. Rasouli, Generalized co-annihilators in residuated lattices, Annals of the University of Craiova, Mathematics and Computer Science Series 45 (2) (2019) 190–207.

[8] M. Sambasiva Rao, Prime filters of commutative $BE$-algebras, J. Appl. Math. Inf. 33 (5–6) (2015) 579–591. https://doi.org/10.14317/jami.2015.579

[9] V.V. Kumar and M.S. Rao, Dual annihilator filters of commutative $BE$-algebras, Asian-European J. Math. 10 (1) (2017) 1750013(11 pages). https://doi.org/10.1142/s1793557117500139

[10] V.V. Kumar and M.S. Rao and S.K. Vali, Regular filters of commutative $BE$-algebras, TWMS J. Appl. & Engg. Math. 11 (4) (2021) 1023–1035.

[11] V.V. Kumar and M.S. Rao, and S.K. Vali, Quasi-complemented $BE$-algebras, Discuss. Math. Gen. Algebra Appl. 41 (2021) 265–281. https://doi.org/10.2307/1996101

[12] A. Walendziak, On commutative $BE$-algebras, Sci. Math. Japon. (2008) 585–588. https://doi.org/10.32219/isms.69.2-281