几类效应代数的张量积及其可表示性

Tensor products of several effect algebras and their representability

研究了几类效应代数的张量积及其可表示性.证明了两个效应代数关于不同的双态射的张量积是同构的,通过构造适当的双态射,给出效应代数{0,1}E、Cm(a)Cn(b)、C2(x)C4(y,z)及C2(x)C′4(y,z)的具体形式,结果表明:{0,1}E是可表示的当且仅当E是可表示的,Cm(a)Cn(b)与C2(x)C4(y,z)都是可表示的效应代数,但C2(x)C′4(y,z)是不可表示的效应代数.

Tensor products of several effect algebras and their representability are discussed.It is proved that any two tensor products of two effect algebras with respect to different bi-morphisms are isomorphic.By constructing proper bi-morphisms,the tensor products of effect algebras{0,1}and E,Cm（a）and Cn （b）,C2 （x）and C4 （y,z）,C2 （x）and C′4 （y,z）are given.Obtained results show that {0,1}E is representable if and only if E is representable,both Cm（a）Cn（b）and C2 （x）C4 （y,z）are representable,but C2 （x）C′4 （y,z）is not representable.