# Complicated BE-algebras and characterizations of ideals

Discussiones Mathematicae - General Algebra and Applications (2015)

- Volume: 35, Issue: 1, page 41-51
- ISSN: 1509-9415

## Access Full Article

top## Abstract

top## How to cite

topYılmaz Çeven, and Zekiye Çiloğlu. "Complicated BE-algebras and characterizations of ideals." Discussiones Mathematicae - General Algebra and Applications 35.1 (2015): 41-51. <http://eudml.org/doc/270295>.

@article{YılmazÇeven2015,

abstract = {In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive and complicated BE-algebra, characterizations of ideals are obtained.},

author = {Yılmaz Çeven, Zekiye Çiloğlu},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {BE-algebras; complicated BE-algebras; ideals in BE-algebras; commutative BE-algebras; bounded BE-algebras},

language = {eng},

number = {1},

pages = {41-51},

title = {Complicated BE-algebras and characterizations of ideals},

url = {http://eudml.org/doc/270295},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Yılmaz Çeven

AU - Zekiye Çiloğlu

TI - Complicated BE-algebras and characterizations of ideals

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2015

VL - 35

IS - 1

SP - 41

EP - 51

AB - In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive and complicated BE-algebra, characterizations of ideals are obtained.

LA - eng

KW - BE-algebras; complicated BE-algebras; ideals in BE-algebras; commutative BE-algebras; bounded BE-algebras

UR - http://eudml.org/doc/270295

ER -

## References

top- [1] J.C. Abbott, Sets, Lattices and Boolean Algebras (Allyn and Bacon, Boston, 1969). Zbl0222.06001
- [2] S.S. Ahn and K.K. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2) (2008) 279-285. Zbl1177.06027
- [3] S.S. Ahn and K.K. So, On generalized upper sets in BE-algebras, Bull. Korean Math. Soc. 46 (2) (2009) 281-287. doi: 10.4134/BKMS.2009.46.2.281 Zbl1171.06306
- [4] S.S. Ahn, Y.H. Kim and J.M. Ko, Filters in commutative BE-algebras, Commun. Korean Math. Soc. 27 (2) (2012) 233-242. doi: 10.4134/CKMS.2012.27.2.233 Zbl1243.06019
- [5] Q.P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11 (2) (1983) 313-320.
- [6] Q.P. Hu and X. Li, On proper BCH-algebras, Math. Japon. 30 (4) (1985) 659-661. Zbl0583.03050
- [7] J. Meng and Y.B. Jun, BCK-algebras (Kyung Moon Sa Co. Seoul-Korea, 1994).
- [8] Y. Imai and K. Iseki, On axiom system of propositional calculi XIV, Proc. Japan Acad. 42 (1966) 19-22. doi: 10.3792/pja/1195522169 Zbl0156.24812
- [9] K. Isėki and S. Tanaka, An introduction to the theory of BCK-Algebras, Math. Japon 23 (1) (1978/79) 1-26. Zbl0385.03051
- [10] K. Isėki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980) 125-130. Zbl0434.03049
- [11] Y.B. Jun, E.H. Roh and H.S. Kim, On BH-algebras, Sci. Math. Japon. 1 (3) (1998) 347-354. Zbl0928.06013
- [12] Y.B. Jun, Y.H. Kim and K.A. Oh, Subtraction algebras with additional conditions, Commun. Korean Math. Soc. 22 (2007) 1-7. Zbl1168.06300
- [13] C.B. Kim and H.S. Kim, On BM-algebras, Sci. Math. Japon 63 (3) (2006) 421-427.
- [14] H.S. Kim and Y.H. Kim, On BE-algebras, Sci. Math. Japon 66 (2007) 113-116.
- [15] H.S. Kim and Y.H. Yon, Dual BCK-algebra and MV-algebra, Sci. Math. Jpn. 66 (2) (2007) 247-353.
- [16] J. Neggers and H.S. Kim, On d-algebras, Math. Slovaca 49 (1999) 19-26.
- [17] J. Neggers, On B-algebras, Mat. Vesnik 54 (1-2) (2002) 21-29.
- [18] J. Neggers, A fundamental theorem of B-homomorphism for B-algebras, Int. Math. J. 2 (3) (2002) 215-219. Zbl1221.06028
- [19] B.M. Schein, Difference Semigroups, Comm. Algebra 20 (1992) 2153-2169. doi: 10.1080/00927879208824453 Zbl0798.20058
- [20] A. Walendziak, Some axiomatizations of B-algebras, Math. Slovaca 56 (3) (2006) 301-306. Zbl1141.06019
- [21] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. 69 (2) (2009) 281-284. Zbl1165.06302
- [22] B. Zelinka, Subtaction Semigroups, Math. Bohemica 120 (1995) 445-447.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.