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Czechoslovak Mathematical Journal, Vol. 55, No. 2, pp. 439-453, 2005
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#
Implicative hyper $K$-algebras

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

* M. M. Zahedi*, Dept. of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran, e-mail: ` zahedi_mm@mail.uk.ac.ir`; * A. Borumand Saeid*, Dept. of Mathematics, Islamic Azad University, Kerman, Iran, e-mail: ` arsham@iauk.ac.ir`; * R. A. Borzooei*, Dept. of Mathematics, Sistan and Baluchestan University, Zahedan, Iran, e-mail: ` borzooei@hamoon.usb.ac.ir`

**Abstract:** In this note we first define the notions of (weak, strong) implicative hyper $K$-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we obtain some relations between these notions and (weak) implicative hyper $K$-ideals. Finally, we study the implicative hyper $K$-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper $K$-algebras and (weak, strong) implicative hyper $K$-algebras under a simple condition.

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

**Classification (MSC 2000):** 06F35, 03G25

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