Complicated BE-algebras and characterizations of ideals
Yılmaz Çeven ; Zekiye Çiloğlu
Discussiones Mathematicae - General Algebra and Applications, Tome 35 (2015), p. 41-51 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270295
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1226,
     author = {Y\i lmaz \c Ceven and Zekiye \c Cilo\u glu},
     title = {Complicated BE-algebras and characterizations of ideals},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {35},
     year = {2015},
     pages = {41-51},
     zbl = {1329.06015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1226}
}
Yılmaz Çeven; Zekiye Çiloğlu. Complicated BE-algebras and characterizations of ideals. Discussiones Mathematicae - General Algebra and Applications, Tome 35 (2015) pp. 41-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1226/

[000] [1] J.C. Abbott, Sets, Lattices and Boolean Algebras (Allyn and Bacon, Boston, 1969). | Zbl 0222.06001

[001] [2] S.S. Ahn and K.K. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2) (2008) 279-285. | Zbl 1177.06027

[002] [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 | Zbl 1171.06306

[003] [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 | Zbl 1243.06019

[004] [5] Q.P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11 (2) (1983) 313-320.

[005] [6] Q.P. Hu and X. Li, On proper BCH-algebras, Math. Japon. 30 (4) (1985) 659-661. | Zbl 0583.03050

[006] [7] J. Meng and Y.B. Jun, BCK-algebras (Kyung Moon Sa Co. Seoul-Korea, 1994).

[007] [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 | Zbl 0156.24812

[008] [9] K. Isėki and S. Tanaka, An introduction to the theory of BCK-Algebras, Math. Japon 23 (1) (1978/79) 1-26. | Zbl 0385.03051

[009] [10] K. Isėki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980) 125-130. | Zbl 0434.03049

[010] [11] Y.B. Jun, E.H. Roh and H.S. Kim, On BH-algebras, Sci. Math. Japon. 1 (3) (1998) 347-354. | Zbl 0928.06013

[011] [12] Y.B. Jun, Y.H. Kim and K.A. Oh, Subtraction algebras with additional conditions, Commun. Korean Math. Soc. 22 (2007) 1-7. | Zbl 1168.06300

[012] [13] C.B. Kim and H.S. Kim, On BM-algebras, Sci. Math. Japon 63 (3) (2006) 421-427.

[013] [14] H.S. Kim and Y.H. Kim, On BE-algebras, Sci. Math. Japon 66 (2007) 113-116.

[014] [15] H.S. Kim and Y.H. Yon, Dual BCK-algebra and MV-algebra, Sci. Math. Jpn. 66 (2) (2007) 247-353.

[015] [16] J. Neggers and H.S. Kim, On d-algebras, Math. Slovaca 49 (1999) 19-26.

[016] [17] J. Neggers, On B-algebras, Mat. Vesnik 54 (1-2) (2002) 21-29.

[017] [18] J. Neggers, A fundamental theorem of B-homomorphism for B-algebras, Int. Math. J. 2 (3) (2002) 215-219. | Zbl 1221.06028

[018] [19] B.M. Schein, Difference Semigroups, Comm. Algebra 20 (1992) 2153-2169. doi: 10.1080/00927879208824453 | Zbl 0798.20058

[019] [20] A. Walendziak, Some axiomatizations of B-algebras, Math. Slovaca 56 (3) (2006) 301-306. | Zbl 1141.06019

[020] [21] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. 69 (2) (2009) 281-284. | Zbl 1165.06302

[021] [22] B. Zelinka, Subtaction Semigroups, Math. Bohemica 120 (1995) 445-447.