On Complemented Subsystems of Commutative Jordan Quadruple Systems  

作　　者：Hader A.Elgendy 

机构地区：[1]Department of Mathematics,Faculty of Science,Damietta University,Damietta 34517,Egypt

出　　处：《Algebra Colloquium》2023年第4期555-568,共14页代数集刊（英文版）

摘　　要：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.

关 键 词：Jordan quadruple system IDEAL complemented subsystem commutative Jordan quadruple system structural projection 

分 类 号：O152[理学—数学]