• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.81-87
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• 2010

We modify the definition of difference algebra given by J. Meng to obtain a structure which is a directoid with sectional switching involutions with respect to the given partial order. Moreover, we show that this is a representation of our skew difference algebras because every such directoid can be converted into a skew difference algebra.