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Bull. Korean Math. Soc. 2003; 40(1): 123-137

Printed March 1, 2003

Copyright © The Korean Mathematical Society.

(Weak) Implicative hyper $K$-ideals

A. Borumand Saeid, R. A. Borzooei, and M. M. Zahedi

Islamic Azad University of Kerman, Sistan and Baluchestan University, Shahid Bahonar University of Kerman

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In this note first we define the notions of weak implicative and implicative hyper $K$-ideals of a hyper $K$-algebra $H$. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we give some relations between these notions and all types of positive implicative hyper $K$-ideals. Finally we classify the implicative hyper $K$-ideals of a hyper $K$-algebra of order 3.

Keywords: hyper $K$-algebra, hyper $K$-ideal, (weak) implicative hyper $K$-ideal

MSC numbers: 06F35, 03G25

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