Complicated BE-algebras and characterizations of ideals

Yılmaz Çeven; Zekiye Çiloğlu

Discussiones Mathematicae - General Algebra and Applications (2015)

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

Abstract

top
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.

How to cite

top

Yılmaz 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. [1] J.C. Abbott, Sets, Lattices and Boolean Algebras (Allyn and Bacon, Boston, 1969). Zbl0222.06001
  2. [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. [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. [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. [5] Q.P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11 (2) (1983) 313-320. 
  6. [6] Q.P. Hu and X. Li, On proper BCH-algebras, Math. Japon. 30 (4) (1985) 659-661. Zbl0583.03050
  7. [7] J. Meng and Y.B. Jun, BCK-algebras (Kyung Moon Sa Co. Seoul-Korea, 1994). 
  8. [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. [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. [10] K. Isėki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980) 125-130. Zbl0434.03049
  11. [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. [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. [13] C.B. Kim and H.S. Kim, On BM-algebras, Sci. Math. Japon 63 (3) (2006) 421-427. 
  14. [14] H.S. Kim and Y.H. Kim, On BE-algebras, Sci. Math. Japon 66 (2007) 113-116. 
  15. [15] H.S. Kim and Y.H. Yon, Dual BCK-algebra and MV-algebra, Sci. Math. Jpn. 66 (2) (2007) 247-353. 
  16. [16] J. Neggers and H.S. Kim, On d-algebras, Math. Slovaca 49 (1999) 19-26. 
  17. [17] J. Neggers, On B-algebras, Mat. Vesnik 54 (1-2) (2002) 21-29. 
  18. [18] J. Neggers, A fundamental theorem of B-homomorphism for B-algebras, Int. Math. J. 2 (3) (2002) 215-219. Zbl1221.06028
  19. [19] B.M. Schein, Difference Semigroups, Comm. Algebra 20 (1992) 2153-2169. doi: 10.1080/00927879208824453 Zbl0798.20058
  20. [20] A. Walendziak, Some axiomatizations of B-algebras, Math. Slovaca 56 (3) (2006) 301-306. Zbl1141.06019
  21. [21] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. 69 (2) (2009) 281-284. Zbl1165.06302
  22. [22] B. Zelinka, Subtaction Semigroups, Math. Bohemica 120 (1995) 445-447. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.