# Quotient hyper pseudo BCK-algebras

Habib Harizavi; Tayebeh Koochakpoor; Rajab Ali Boorzoei

Discussiones Mathematicae - General Algebra and Applications (2013)

- Volume: 33, Issue: 2, page 147-165
- ISSN: 1509-9415

## Access Full Article

top## Abstract

top## How to cite

topHabib Harizavi, Tayebeh Koochakpoor, and Rajab Ali Boorzoei. "Quotient hyper pseudo BCK-algebras." Discussiones Mathematicae - General Algebra and Applications 33.2 (2013): 147-165. <http://eudml.org/doc/270358>.

@article{HabibHarizavi2013,

abstract = {In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.},

author = {Habib Harizavi, Tayebeh Koochakpoor, Rajab Ali Boorzoei},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {hyper pseudo BCK-algebra; normal hyper pseudo BCK-ideal; quotient hyper pseudo BCK-algebra; hyper pseudo BCK-algebras; hyper pseudo BCK-ideals; regular congruences},

language = {eng},

number = {2},

pages = {147-165},

title = {Quotient hyper pseudo BCK-algebras},

url = {http://eudml.org/doc/270358},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Habib Harizavi

AU - Tayebeh Koochakpoor

AU - Rajab Ali Boorzoei

TI - Quotient hyper pseudo BCK-algebras

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2013

VL - 33

IS - 2

SP - 147

EP - 165

AB - In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.

LA - eng

KW - hyper pseudo BCK-algebra; normal hyper pseudo BCK-ideal; quotient hyper pseudo BCK-algebra; hyper pseudo BCK-algebras; hyper pseudo BCK-ideals; regular congruences

UR - http://eudml.org/doc/270358

ER -

## References

top- [1] R.A. Borzooei and H. Harizavi, Regular Congruence Relations on Hyper BCK-algebras, Sci. Math. Jap. 61 (2005) 217-231. Zbl1067.06016
- [2] R.A. Borzooei, A. Hasankhani, M.M. Zahedi and Y.B. Jun, On hyper K-algebra, Math. Jap. 52 (2000) 113-121.
- [3] R.A. Borzooei, A. Rezazadeh and R. Ameri, On hyper pseudo BCK-algebra, Iranian J. Math. Sci. and Inf., to appear. Zbl1306.06017
- [4] R.A. Borzooei, M.M. Zahedi and H. Rezaei, Classification of hyper BCK-algebras of order 3, Italian J. Pure Appl. Math. 12 (2002) 175-184. Zbl1169.06301
- [5] P. Corsini and V. Leoreanu, Applications of Hyper Structure Theory (Kluwer Academic Publications, 2003). doi: 10.1007/978-1-4757-3714-1. Zbl1027.20051
- [6] G. Ggeorgesu and A. Iorulescu, Pseudo BCK-algebra, in: Proceeding of DMTCS 01, Combinatorics and Logic (Ed(s)), (Springer London, 2001) 97-114.
- [7] Sh. Ghorbani, A. Hasankhani and E. Eslami, Hyper MV-algebras, Set-Valued Mathematics and Applications 1 (2008) 205-222.
- [8] A. Iorgulescu, Classes of Pseudo BCK-algebra-Part I, Journal of Multiple-valued Logic and Soft Computing 12 (2006) 71-130.
- [9] A. Iorgulescu, Classes of Pseudo BCK-algebra-Part II, Journal of Multiple-valued Logic and Soft Computing 12 (2006) 575-629.
- [10] Y. Imai and K. Iseki, On Axiom System of Prepositional Calculi XIV, Proc. Japan Acad. 42 (1996) 26-29.
- [11] Y.B. Jun, M. Kondo and K.H. Kim, Pseudo Ideals of Pseudo BCK-algebras, Sci. Math. Jap. 8 (2003) 87-91.
- [12] Y.B. Jun, M.M. Zahedi, X.L. Xin and R.A. Borzooei, On Hyper BCK-algebra, Italian J. Pure and Appl. Math. 10 (2000) 127-136. Zbl1008.06014
- [13] F. Marty, Scu une généralization de la notion de groups, in: 8th Congress Math. (Ed(s)), (Scandinavian, Stockholm, 1934) 45-49.
- [14] Jie Meng and Young Bae Jun, BCK-algebras (Kyung Moon Sa. Co., 1994).

## NotesEmbed ?

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