DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

M. Sambasiva Rao

M. Sambasiva Rao

Department of Mathematics
MVGR College of Engineering
Vizianagaram, India-535005

email: msraomaths35@rediffmail.com

Title:

$\sigma$-filters of commutative $BE$-algebras

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 121-134

Received: 2021-07-13 , Revised: 2021-11-04 , Accepted: 2021-11-04 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1417

Abstract:

The concept of $\sigma $-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 $\sigma $-filter. Some necessary and sufficient conditions are given for every regular filter of a commutative $BE$-algebra to become a $\sigma $-filter. A set of equivalent conditions is given for the class of all $\sigma $-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

References:

  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
Close