# On Isomorphisms of KU-algebras

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```					   Scientia Magna
Vol. 5 (2009), No. 3, 25-31

On Isomorphisms of KU-algebras
Chanwit Prabpayak† and Utsanee Leerawat‡

†Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon,
Bangkok, Thailand
‡Department of Mathematics, Kasetsart University, Bangkok, Thailand
E-mail: chanwit.p@rmutp.ac.th fsciutl@ku.ac.th

Abstract In this paper, we study homomorphisms of KU-algebras and investigate its prop-
erties. Moreover, some consequences of the relations between quotient KU-algebras and iso-
morphisms are shown.
Keywords Homomorphism, isomorphism, ideal, congruence, KU-algebras.

§1. Introduction
In [3], C. Prabpayak and U. Leerawat studied ideals and congruences of BCC-algebras
([1],[2]) and introduced a new algebraic structure which is called KU-algebras. They gave
the concept of homomorphisms of KU-algebras and investigated some related properties. The
purpose of this paper is to derive some straightforward consequences of the relations between
quotient KU-algebras and isomorphisms and also investigate some of its properties.

§2. Preliminaries
A nonempty set G with a constant 0 and a binary operation denoted by juxtaposition is
called a KU-algebra if for all for all x, y, z ∈ G the following conditions hold:
(1) (xy)((yz)(xz)) = 0,
(2) 0x = x,
(3) x0 = 0,
(4) xy = 0 = yx implies x = y,
for all x, y, z ∈ G.
By (1), we get (00)((0x)(0x)) = 0. It follows that xx = 0 for all x ∈ G. And if we put
y = 0 in (1), then we obtain z(xz) = 0 for all x, z ∈ G.
A subset S of a KU-algebra G is called subalgebra of G if xy ∈ S whenever x, y ∈ S.
A non-empty subset A of a KU-algebra G is called an ideal of G if it satisﬁes the following
conditions:

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Description: In this paper, we study homomorphisms of KU-algebras and investigate its properties. Moreover, some consequences of the relations between quotient KU-algebras and isomorphisms are shown. [PUBLICATION ABSTRACT]
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