• Journal of Convergence for Information Technology
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• v.7 no.3
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• pp.65-71
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• 2017

The quantum logic was introduced by G. Birkhoff and 1. von Neumann in order to study projections of a Hilbert space for a formulation of quantum mechanics, and Husimi proposed orthomodular law and orthomodular lattices to complement the quantum logic. Abott introduced orthoimplication algebras and its properties to investigate an implication of orthomodular lattice. The commuting relation is an important property on orthomodular lattice which is related with the distributive law and the modular law, etc. In this paper, we define a binary operation on orthoimplication algebra and the greatest lower bound by using this operation and research some properties of this operation. Also we define a homomorphism and characterize the commuting relation of orthoimplication algebra by the homomorphism.