Geodesic
On pseudo BE-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 95-108.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: BE-algebra, Pseudo BE-algebra, pseudo filter, pseudo upper set 
@article{DMGAA_2013_33_1_a6,
     author = {Borzooei, Rajab and Saeid, Arsham and Rezaei, Akbar and Radfar, Akefe and Ameri, Reza},
     title = {On pseudo {BE-algebras}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {95--108},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a6/}
}
TY  - JOUR
AU  - Borzooei, Rajab
AU  - Saeid, Arsham
AU  - Rezaei, Akbar
AU  - Radfar, Akefe
AU  - Ameri, Reza
TI  - On pseudo BE-algebras
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2013
SP  - 95
EP  - 108
VL  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a6/
LA  - en
ID  - DMGAA_2013_33_1_a6
ER  - 
%0 Journal Article
%A Borzooei, Rajab
%A Saeid, Arsham
%A Rezaei, Akbar
%A Radfar, Akefe
%A Ameri, Reza
%T On pseudo BE-algebras
%J Discussiones Mathematicae. General Algebra and Applications
%D 2013
%P 95-108
%V 33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a6/
%G en
%F DMGAA_2013_33_1_a6
Borzooei, Rajab; Saeid, Arsham; Rezaei, Akbar; Radfar, Akefe; Ameri, Reza. On pseudo BE-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 95-108. http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a6/

[1] S.S. Ahn and Y.H. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2) (2008) 279-285.

[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

[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

[4] A. Borumand Saeid, A. Rezaei and R.A. Borzoei, Some types of filters in BE-algebras, (submitted).

[5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, Information Technology (Bucharest, 1999), 961-968, Inforec, Bucharest.

[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] 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.

[8] Y. Imai and K. Iseki, On axiom systems of propositional Calculi, XIV proc. Jpn. Academy 42 (1966) 19-22.

[9] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pesudo-BCI algebras, Math. Bec. 58 (2006) 39-46.

[10] H.S. Kim and Y.H. Kim, On BE-algebras, Sci, Math, Jpn. 66 (1) (2007) 113-117.

[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

[12] B.L. Meng, On filters in BE-algebras, Sci. Math. Jpn. 71 (2010), 201-207.

[13] J. Rachunek, A non commutative generalization of MV-algebras, Czehoslovak Math. J. 52 (127) (2002) 255-273.

[14] A. Rezaei and A. Borumand Saeid, Some results in BE-algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX (2012), 33-44.

[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

[16] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. 69 (2) (2008) 585-588.

[17] A. Walendziak, On axiom systems of pseudo-BCK algebras, Bull. Malays. Math. Sci. Soc. 34 (2) (2011) 287-293.