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 commut...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.展开更多
文摘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.
