# 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

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topRajab 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] 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] 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] 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] 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. Zbl0985.06007
- [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. Zbl0986.06018
- [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. Zbl1119.03068
- [10] H.S. Kim and Y.H. Kim, On BE-algebras, Sci, Math, Jpn. 66 (1) (2007) 113-117. Zbl1137.06306
- [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] B.L. Meng, On filters in BE-algebras, Sci. Math. Jpn. 71 (2010), 201-207. Zbl1193.06021
- [13] J. Rachunek, A non commutative generalization of MV-algebras, Czehoslovak Math. J. 52 (127) (2002) 255-273. Zbl1012.06012
- [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] 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] 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. Zbl1222.06010

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