Minimal prime filters of commutative $BE$-algebras

Document Type : Research Paper

Authors

1 Department of mathematics, Aditya Engineering College, Surampalem Andhra Pradesh, India.

2 Department of mathematics, MVGR College of Engineering, Vizianagaram Andhra Pradesh, India.

3 Department of mathematics, JNTUK University College of Engineering, Vizianagaram Andhra Pradesh, India.

Abstract

In this paper we introduced the concept of minimal prime filters in commutative $BE$-algebras. A characterization theorem for minimal prime filters of $BE$-algebras is derived. Some properties of minimal prime filters of a commutative $BE$-algebras are derived with the help of congruences. A necessary and sufficient is derived for a pair of minimal prime filters to become co-maximal.

Keywords


[1] S. S. Ahn, Y. H. Kim and J. M. Ko, Filters in commutative BE-algebras, Commun. Korean. Math. Soc., 27 No. 2 (2012) 233-242.
[2] A. Borumand Saeid, A. Rezaei and R. A. Borzooei, Some types of filters in BE-algebras, Math. Comput. Sci., 7 (2013) 341-352.
[3] K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Jpn., 23 No. 1 (1979) 1-26.
[4] H. S. Kim and Y. H. Kim, On BE-algebras, Sci. Math. Jpn. Online., e-2006 (2006) 1299-1302.
[5] B. L. Meng, On filters in BE-algebras, Sci. Math. Jpn., 71 No. 2 (2010) 105-111.
[6] J. Meng, BCK-filters, Math. Japonica., 44 No.1 (1996) 119-129.
[7] J. Meng, Y. B. Jun and X. L. Xin, Prime ideals in commutative BCK-algebras, Discus. Math., 18 (1998) 5-15.
[8] A. Rezaei, A. Borumand Saeid and R. A. Borzooei, KU-algebras are equivalent to commutative self distributive BE-algebras, Bollettino di Matematica pura e Applicata., 7 (2014) 1-8.
[9] A. Rezaei and A. Borumand Saeid, Relation between BE-algebras and g-Hilbert algebras, Discuss. Math.-Gen. Algebra Appl., 38 No. 1 (2018) 33-45.
[10] M. Sambasiva Rao, Prime filters of commutative BE-algebras, J. Appl. Math. & Inform., 33 No. 5-6 (2015) 579-591.
[11] V. Venkata Kumar and M. Sambasiva Rao, Dual annihilator filters of commutative BE-algebras, Asian-European j. Math., 10 No. 01 (2017) 1750013.
[12] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn., 69 No. 2 (2008) 585-588.