Hyper BCI-algebras

• Autorzy: Xiao Long Xin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hyper BCI-algebra; hyper group; hyper $H_{v}$-group

Kategorie tematyczne

• 06F35: BCK-algebras, BCI-algebras
• 03G25: Other algebras related to logic
• 20N20: Hypergroups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 5-19

Daty

wydano

2006

otrzymano

2004-01

poprawiono

2005-09

Twórcy

autor

Xiao Long Xin

• Department of Mathematics, Northwest University, Xian 710069, P. R. China

Bibliografia

• [1] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore 1993.
• [2] K. Iséki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon. 21 (1976), 351-366
• [3] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. (1) 23 (1978), 1-26.
• [4] Y.B. Jun and X.L. Xin, Scalar elements and hyperatoms of hyper BCK-algebras, Scientiae Mathematicae (3) 2 (1999), 303-309
• [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
• [8] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49.
• [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.

Identyfikatory

DOI

10.7151/dmgaa.1102