# Hyper BCI-algebras

Discussiones Mathematicae - General Algebra and Applications (2006)

- Volume: 26, Issue: 1, page 5-19
- ISSN: 1509-9415

## Access Full Article

top## Abstract

top## How to cite

topXiao Long Xin. "Hyper BCI-algebras." Discussiones Mathematicae - General Algebra and Applications 26.1 (2006): 5-19. <http://eudml.org/doc/276842>.

@article{XiaoLongXin2006,

abstract = {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 $H_\{v\}$-groups.},

author = {Xiao Long Xin},

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

keywords = {hyper BCI-algebra; hyper group; hyper $H_\{v\}$-group; hyper BCI-algebra, hypergroup; hyper -group},

language = {eng},

number = {1},

pages = {5-19},

title = {Hyper BCI-algebras},

url = {http://eudml.org/doc/276842},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Xiao Long Xin

TI - Hyper BCI-algebras

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2006

VL - 26

IS - 1

SP - 5

EP - 19

AB - 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 $H_{v}$-groups.

LA - eng

KW - hyper BCI-algebra; hyper group; hyper $H_{v}$-group; hyper BCI-algebra, hypergroup; hyper -group

UR - http://eudml.org/doc/276842

ER -

## References

top- [1] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore 1993. Zbl0785.20032
- [2] K. Iséki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon. 21 (1976), 351-366 Zbl0355.02041
- [3] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. (1) 23 (1978), 1-26. Zbl0385.03051
- [4] Y.B. Jun and X.L. Xin, Scalar elements and hyperatoms of hyper BCK-algebras, Scientiae Mathematicae (3) 2 (1999), 303-309 Zbl0967.06016
- [5] Y.B. Jun and X.L. Xin, Positive implicative hyper BCK-algebras, Scientiae Mathematicae Japonicae Online 5 (2001), 67-76
- [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
- [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 Zbl1008.06014
- [8] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49. Zbl61.1014.03
- [9] J. Meng and Y.B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea 1994.
- [10] M.M. Zahedi and A. Hasankhani, F-polygroups (I), J. Fuzzy Math. 3 (1996), 533-548
- [11] T. Vougiouklis, A new class of hyperstructure, J. Comb. Inf. Syst. Sciences.

## NotesEmbed ?

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