Document Type : Original Manuscript

Authors

1 Department of Mathematics, University of SHAHED, Tehran, Iran.

2 Department of Mathematics, University of SHAHED, P.O.Box 18151-159, Tehran, Iran.

10.22044/jas.2020.8717.1423

Abstract

In the present manuscript, we introduce a type of hyper K-algebra which is called left absorbing hyper K-algebra and investigate some of the related properties. We also show that set of all types of positive implicative and commutative hyper K-ideal form a distributive latttice and study their diagrams when positive implicative and commutative hyper K-ideal are a hyper K-ideal and the hyper K-algebra is left absorbing.

Keywords

1. A. Boromand saeid, R. A. Borzooei and M. M. Zahedi, (Weak) implicative hyper K-ideal, Bull. Korean Math. Soc., 40 (2003), 123–137.


2. R. A. Borzooei, M. Bakhshi, Lattices Structures on Ideals of a BCK-algebras, J. MULT-VALUED LOG. S., 18 (2012), 387–399.


3. R. A. Borzooei, A. Hasankhani, M. M. Zahedi, and Y. B. Jun, On hyper Kalgebras, Sci. Math. Jpn., 52(1) (2000), 113–121.

 

4. Y. Imai and K. Iséki, On axiom systems of propositional calculi xiv, Proc. Japan Academi, 42 (1966), 19–22.


5. Y. B. Jun, x. L. xin, E. H. Roh, and M. M. Zahedi, Strong on hyper BCK-ideals of hyper BCK-algebras, Math. Japon., 51(3) (2000), 493–498.


6. Vijay K. Khanna, Lattices and boolean algebras, Vikas Publishing House Pvt Ltd, 1994.


7. F. Marty, Sur une generalization de la notion de groups, 8th congress Math Scandinavies, Stockhholm, (1934), 45–49.


8. M. A. Nasr-Azadani and M. M. Zahedi, Quasi union hyper K- algebras, Quasigroups Relat. Syst., 16 (2008), 77–88.


9. T. Roodbari and M. M. Zahedi, Positive implicative hyper K-ideals II, Mathematica Japonicae Online, e(2007), 507–520.


10. T. Roodbari and L. Torkzadeh and M. M. Zahedi, Simple hyper K-algebras, Quasigroups Relat. Syst., 16 (2008), 131–140.


11. M. M. Zahedi, R. A. Borzooei, Y. B. Jun, and A. Hasankhani, Some results on hyper K-algebra, Sci. Math. Jpn., 3(1) (2000), 53–59.