On pseudo BE-algebras

Rajab Ali Borzooei; Arsham Borumand Saeid; Akbar Rezaei; Akefe Radfar; Reza Ameri

Discussiones Mathematicae - General Algebra and Applications (2013)

  • Volume: 33, Issue: 1, page 95-108
  • ISSN: 1509-9415

Abstract

top
In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.

How to cite

top

Rajab Ali Borzooei, et al. "On pseudo BE-algebras." Discussiones Mathematicae - General Algebra and Applications 33.1 (2013): 95-108. <http://eudml.org/doc/270638>.

@article{RajabAliBorzooei2013,
abstract = {In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.},
author = {Rajab Ali Borzooei, Arsham Borumand Saeid, Akbar Rezaei, Akefe Radfar, Reza Ameri},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {BE-algebra; Pseudo BE-algebra; pseudo filter; pseudo upper set; pseudo BE-algebras; pseudo subalgebras; pseudo filters; pseudo upper sets},
language = {eng},
number = {1},
pages = {95-108},
title = {On pseudo BE-algebras},
url = {http://eudml.org/doc/270638},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Rajab Ali Borzooei
AU - Arsham Borumand Saeid
AU - Akbar Rezaei
AU - Akefe Radfar
AU - Reza Ameri
TI - On pseudo BE-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2013
VL - 33
IS - 1
SP - 95
EP - 108
AB - In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.
LA - eng
KW - BE-algebra; Pseudo BE-algebra; pseudo filter; pseudo upper set; pseudo BE-algebras; pseudo subalgebras; pseudo filters; pseudo upper sets
UR - http://eudml.org/doc/270638
ER -

References

top
  1. [1] S.S. Ahn and Y.H. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2) (2008) 279-285. Zbl1177.06027
  2. [2] S.S. Ahn and K.S. 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
  3. [3] S.S. Ahn, Y.H. Kim and J.M. Ko, Filters in commutative BE-algebras, Bull. Korean Math. Soc. 27 (2) (2012) 233-242. doi: 10.4134/CKMS.2012.27.2.233 Zbl1243.06019
  4. [4] A. Borumand Saeid, A. Rezaei and R.A. Borzoei, Some types of filters in BE-algebras, (submitted). 
  5. [5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, Information Technology (Bucharest, 1999), 961-968, Inforec, Bucharest. Zbl0985.06007
  6. [6] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, in Abstracts of the Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92. 
  7. [7] G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK-algebras, Combinatorics, computability and logic, 97-114, Springer Ser. Discrete Math. Theor. Comput. Sci., Springer, London, 2001. Zbl0986.06018
  8. [8] Y. Imai and K. Iseki, On axiom systems of propositional Calculi, XIV proc. Jpn. Academy 42 (1966) 19-22. 
  9. [9] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pesudo-BCI algebras, Math. Bec. 58 (2006) 39-46. Zbl1119.03068
  10. [10] H.S. Kim and Y.H. Kim, On BE-algebras, Sci, Math, Jpn. 66 (1) (2007) 113-117. Zbl1137.06306
  11. [11] Y.H. Kim and K.S. So, On minimality in pseudo-BCI algebras, Commun. Korean Math. Soc. 27 (1) (2012) 7-13. doi: 10.4134/CKMS.2012.27.1.007 Zbl1244.06008
  12. [12] B.L. Meng, On filters in BE-algebras, Sci. Math. Jpn. 71 (2010), 201-207. Zbl1193.06021
  13. [13] J. Rachunek, A non commutative generalization of MV-algebras, Czehoslovak Math. J. 52 (127) (2002) 255-273. Zbl1012.06012
  14. [14] A. Rezaei and A. Borumand Saeid, Some results in BE-algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX (2012), 33-44. Zbl1289.06034
  15. [15] A. Rezaei and A. Borumand Saeid, Commutative ideals in BE-algebras, Kyungpook Math. J. 52 (2012) 483-494. doi: 10.5666/KMJ.2012.52.4.483 Zbl1284.06058
  16. [16] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. 69 (2) (2008) 585-588. 
  17. [17] A. Walendziak, On axiom systems of pseudo-BCK algebras, Bull. Malays. Math. Sci. Soc. 34 (2) (2011) 287-293. Zbl1222.06010

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.