首页|On Complemented Subsystems of Commutative Jordan Quadruple Systems
On Complemented Subsystems of Commutative Jordan Quadruple Systems
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We extend the notions of commutativity,ideals,anisotropy,and complemented subtriples of Jordan triple systems to those of Jordan quadruple systems.We show that if S is a complemented subsystem of an anisotropic commutative Jordan quadruple system U,then S and its annihilator S⊥ are orthogonal ideals and U=S ⊕ S⊥.We also prove that the range of a structural projection on an anisotropic commutative Jordan quadruple system is a complemented ideal and,conversely,a complemented subsystem of an anisotropic commutative Jordan quadruple system is the range of a unique structural projection.
Jordan quadruple systemidealcomplemented subsystemcommutative Jordan quadruple systemstructural projection
Hader A.Elgendy
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Department of Mathematics,Faculty of Science,Damietta University Damietta 34517,Egypt
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