Hyper BCI-algebras

Xiao Long Xin

Discussiones Mathematicae - General Algebra and Applications (2006)

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

Abstract

top
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.

How to cite

top

Xiao 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. [1] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore 1993. Zbl0785.20032
  2. [2] K. Iséki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon. 21 (1976), 351-366 Zbl0355.02041
  3. [3] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. (1) 23 (1978), 1-26. Zbl0385.03051
  4. [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. [5] Y.B. Jun and X.L. Xin, Positive implicative hyper BCK-algebras, Scientiae Mathematicae Japonicae Online 5 (2001), 67-76 
  6. [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. [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. [8] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49. Zbl61.1014.03
  9. [9] J. Meng and Y.B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea 1994. 
  10. [10] M.M. Zahedi and A. Hasankhani, F-polygroups (I), J. Fuzzy Math. 3 (1996), 533-548 
  11. [11] T. Vougiouklis, A new class of hyperstructure, J. Comb. Inf. Syst. Sciences. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.