We introduce the concept of a hyper BCI-algebra which is a generalization of a BCI-algebra, and investigate some related properties. Moreover we introduce a hyper BCI-ideal, weak hyper BCI-ideal, strong hyper BCI-ideal and reflexive hyper BCI-ideal in hyper BCI-algebras, and give some relations among these hyper BCI-ideals. Finally we discuss the relations between hyper BCI-algebras and hyper groups, and between hyper BCI-algebras and hyper -groups.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1102, author = {Xiao Long Xin}, title = {Hyper BCI-algebras}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {26}, year = {2006}, pages = {5-19}, zbl = {1101.06016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1102} }
Xiao Long Xin. Hyper BCI-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 5-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1102/
[000] [1] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore 1993. | Zbl 0785.20032
[001] [2] K. Iséki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon. 21 (1976), 351-366 | Zbl 0355.02041
[002] [3] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. (1) 23 (1978), 1-26. | Zbl 0385.03051
[003] [4] Y.B. Jun and X.L. Xin, Scalar elements and hyperatoms of hyper BCK-algebras, Scientiae Mathematicae (3) 2 (1999), 303-309 | Zbl 0967.06016
[004] [5] Y.B. Jun and X.L. Xin, Positive implicative hyper BCK-algebras, Scientiae Mathematicae Japonicae Online 5 (2001), 67-76
[005] [6] Y.B. Jun, X.L. Xin, E.H. Roh and M.M. Zahedi, Strong hyper BCK-ideals of hyper BCK-algebras, Math. Japon. (3) 51 (2000), 493-498
[006] [7] Y.B. Jun, M.M. Zahedi, X.L. Xin and R.A. Borzoei, On hyper BCK-algebras, Italian J. Pure and Appl. Math. 8 (2000), 127-136 | Zbl 1008.06014
[007] [8] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49. | Zbl 61.1014.03
[008] [9] J. Meng and Y.B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea 1994.
[009] [10] M.M. Zahedi and A. Hasankhani, F-polygroups (I), J. Fuzzy Math. 3 (1996), 533-548
[010] [11] T. Vougiouklis, A new class of hyperstructure, J. Comb. Inf. Syst. Sciences.