Paper

Mathware & Soft Computing 13 (2006) 37-58

Dual Commutative Hyper K-Ideals of typesetters case 1 in Hyper K-algebras of Order 3
L. Torkzadeh1 and M.M. Zahedi2 1 Dept. Math., Islamic Azad Univ. of Kerman, Kerman, Iran Dept. Math., Shahid Bahonar Univ. of Kerman, Kerman, Iran ltorkzadeh@yahoo.com zahedi mm@mail.uk.ac.ir, http://math.uk.ac.ir/?zahedi
Abstract In this note we classify the bound hyper K-algebras of order 3, which have D1 = {1}, D2 = {1, 2} and D3 = {0, 1} as a doubled commutative hyper K-ideal of type 1. In this pick up we show that there are such non-isomorphic bounded hyper K-algebras. 2000 maths Subject Classi?cation. 03B47, 06F35, 03G25 Key words and phrases: hyper K-algebra, dual commutative hyper K-ideal.

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1

Introduction

The hyperalgebraic social structure theory was introduced by F. Marty [5] in 1934. Imai and Iseki [3] in 1966 introduced the notion of a BCK-algebra. Borzooei, Jun and Zahedi et.al. [2,8] applied the hyperstructure to BCK-algebras and introduced the concept of hyper K-algebra which is a generalization of BCK-algebra. In [7]we de?ned the notions of dual commutative hyper K-ideals of type 1 and type 2 (Brie?y DCHKI ? T 1, T 2). Now we follow it and determine each(prenominal) bounded hyper K-algebras of order 3 which have DCIHKI ? T 1.

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Preliminaries

De?nition 2.1.



[2] permit H be a nonempty set and ? be a hyperoperation on H, that is ? is a function from H × H to P ? (H) = P(H){?}. thence H is called a hyper K-algebra if it contains a constant 0 and satis?es the following axioms: (HK1) (x ? z) ? (y ? z) < x ? y (HK2) (x ? y) ? z = (x ? z) ? y (HK3) x < x 37

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L. Torkzadeh & M.M. Zahedi

(HK4) x < y, y < x ? x = y (HK5) 0 < x, for all x, y, z ? H, where x < y is de?ned by 0 ? x ? y and for every A, B ? H, A < B is de?ned by ?a ? A, ?b ? B such that a < b. Note that if A, B ? H, then by A ? B we mean the subset a ? b of H.
a?A b?B

Theorem 2.2. [2] Let (H, ?, 0) be a hyper K-algebra. Then for all x, y, z ? H and for...If you want to get a full essay, order it on our website: Orderessay



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