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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1205, author = {Habib Harizavi and Tayebeh Koochakpoor and Rajab Ali Boorzoei}, title = {Quotient hyper pseudo BCK-algebras}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {33}, year = {2013}, pages = {147-165}, zbl = {1303.06024}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1205} }
Habib Harizavi; Tayebeh Koochakpoor; Rajab Ali Boorzoei. Quotient hyper pseudo BCK-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013) pp. 147-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1205/
[000] [1] R.A. Borzooei and H. Harizavi, Regular Congruence Relations on Hyper BCK-algebras, Sci. Math. Jap. 61 (2005) 217-231. | Zbl 1067.06016
[001] [2] R.A. Borzooei, A. Hasankhani, M.M. Zahedi and Y.B. Jun, On hyper K-algebra, Math. Jap. 52 (2000) 113-121.
[002] [3] R.A. Borzooei, A. Rezazadeh and R. Ameri, On hyper pseudo BCK-algebra, Iranian J. Math. Sci. and Inf., to appear. | Zbl 1306.06017
[003] [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. | Zbl 1169.06301
[004] [5] P. Corsini and V. Leoreanu, Applications of Hyper Structure Theory (Kluwer Academic Publications, 2003). doi: 10.1007/978-1-4757-3714-1. | Zbl 1027.20051
[005] [6] G. Ggeorgesu and A. Iorulescu, Pseudo BCK-algebra, in: Proceeding of DMTCS 01, Combinatorics and Logic (Ed(s)), (Springer London, 2001) 97-114.
[006] [7] Sh. Ghorbani, A. Hasankhani and E. Eslami, Hyper MV-algebras, Set-Valued Mathematics and Applications 1 (2008) 205-222.
[007] [8] A. Iorgulescu, Classes of Pseudo BCK-algebra-Part I, Journal of Multiple-valued Logic and Soft Computing 12 (2006) 71-130.
[008] [9] A. Iorgulescu, Classes of Pseudo BCK-algebra-Part II, Journal of Multiple-valued Logic and Soft Computing 12 (2006) 575-629.
[009] [10] Y. Imai and K. Iseki, On Axiom System of Prepositional Calculi XIV, Proc. Japan Acad. 42 (1996) 26-29.
[010] [11] Y.B. Jun, M. Kondo and K.H. Kim, Pseudo Ideals of Pseudo BCK-algebras, Sci. Math. Jap. 8 (2003) 87-91.
[011] [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. | Zbl 1008.06014
[012] [13] F. Marty, Scu une généralization de la notion de groups, in: 8th Congress Math. (Ed(s)), (Scandinavian, Stockholm, 1934) 45-49.
[013] [14] Jie Meng and Young Bae Jun, BCK-algebras (Kyung Moon Sa. Co., 1994).