【摘要】 给出数域F上线性空间的一类更一般的统一框架 ,即广义线性空间的概念 :设T是论域 ,F是数域 ,V(T) ={ρ｜ρ:T→F}, ρ ,σ∈V(T) , a∈F ,规定 ( ρ + σ) (x) =ρ(x) +σ(x) ,(aρ) (x) =a( ρ(x) ) ,则V(T)为F上的广义线性空间 .在该框架下引入半序关系 ,构造一类半序线性空间 (V ,≤ ) : α ,β ,γ ∈V , a∈F ,若α≤ β ,则1 )α+γ≤ β+γ且γ +α≤γ+ β ;2 )当a≥ 0时 ,aα≤aβ,当a <0时 ,aβ≤aα .同时构造了分子概念 :格L中的元素a称为并既约元 ,若 x ,y∈L ,a=x∨y,则a=x或a=y ,L中非最小元的并既约元称为L中的分子 .并讨论其分子结构 ,从而为进一步探讨线性空间上的代数结构、序结构及拓扑结构的复合结构奠定理论基础更多还原

【Abstract】 Belong to the number field F to the linear space of the type is more general of unify the frame, namely the concept of the generali zed linear space: let T is the set, F is the number field, V(T)={ρ| ρ:T→F},ρ,σ∈V(T),a∈F ,provision ( ρ+σ)(x)=ρ(x)+σ(x),(aρ)(x)=a( ρ(x)) ,then V(T) is the generalized linear space on the F . Under the f rame estabished the ordered relation and ordered_linear space V(T):α,β,γ ∈V,a∈F ,if α≤β, then 1) α+γ≤β+γ and γ+α≤γ+β ;2)When a ≥0 hour, aα≤a β ,be the a<0 hour, aβ≤aα . Constructed the numerator concept at the same time: the element in the lattice L is called the joint_irreducible ele ment if and only if x,y∈L,a=x∨y , then a=x or a=y , the joint_irr educible element that isnt minimal element in the L is called the numerato r in the L . And discussed the construction of its numerator, hence for furt her study the reunited_structure of the algebra_structure, the ordered_structure and the topological_structure builded the theory base.更多还原