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With the deepening of the research of Hopf algebras , the concept of the Hopf al-gebra's weak meaning is becoming more and more understood and valued. Somesimple properties of weak Hopf algebras and some specific examples about weakHopf algebras are studied in this paper. And some Homomorphism propertiesand some examples are also investigated. A new class of weak Hopf module isPresented, and the fundamental theorem of homomorphism of weak Hopf alge-bras is extended to the new weak Hopf modules. Thereby it has a further studyof the invariant properties of weak Hopf modules.First of all, according the definition of weak Hopf modules , some examplesand the properties in references [3],[23], we get some simple properties of weakHopf algebras.Secondly, by using Hopf algebras using the Functional properties lemma ofweak Hopf algebras, we discuss the relationship between the integrals and an-tipode element of the weak Hopf algebras homomorphism and weak Hopf al-gebras .Finally, a valued example of weak Hopf algebras is presented, and someproperties of weak Hopf algebras is discussing by using the example. The thesisis divided into the four parts as follows:Section 1 gets some conclusions of weak Hopf algebras . The main results arebelow:Theorem1.1.1 Set H be an arbitrary weak Hopf algebras, for (?)h,h∈H then:(1)h R (h ) = h(1)ε(h(2)S(h ))(2) L(h)h =ε(S(h)h(1))h(2)Example1.2.2 Set H be an arbitrary weak Hopf algebras, A be right H(?)comodule coalgebra. Let C = A (?) H, then C can be weak bialgebra if defines anoperation appropriately.Example1.2.3 Set (H, M, u, (?),ε, S)be weak Hopf algebras, A H be aH's K(?) subspace, then(1) if (A,M|A(?)A, u)be an algebras, (A, (?)|A,εA)be a coalgebra, then(A,M|A(?)A,u, (?)|A,εA) be a weak bialgebras. (2) if A be H's ideal, and also be H's coideal, and S(A) (?) A, then H/A beweak Hopf algebras.Section 2 gets some conclusions of weak Hopf algebras homomorphism. Themain results are below:Theorem2.1.1: Set H₁, H₂, H₃ be weak Hopf algebras, f1 : H₁→H₂ f2 :H₂→H₃ be weak Hopf algebras homomorphism, then f1f2 : H₁→H₃ also beweak Hopf algebras homomorphism.Theorem2.1.2 Set H be a weak Hopf algebras; A be H's ideal,and alsobe H's coideal, and S(A) (?) A, thenÏ€: H→H/A be weak Hopf algebrashomomorphism.Theorem2.2.1 Set f : H→B be a weak simple Hopf algebras homomor-phism, then for (?)l∈S L(H), (?)b∈B we have f(l(1)) (?) bf(l(2)) = S(b)f(l(1)) (?)f(l(2)).Theorem2.2.2 Set SH,SB be H,Bweak Hopf algebra's anti-pode,and f :H→B be weak Hopf algebras homomorphism, then MB(SBf (?) f)(?)H =MB(fSH (?) f)(?)H.Theorem2.3.1 In the dual weak bialgebras [H, K,σ],(1) if H be a weak Hopf algebras, thenσConvolution invertible, andσ(?)1 =σ(SH (?) 1)(2) if K be a weak Hopf algebra, thenσConvolution invertible, andσ(?)1 =σ(1 (?) SK)Theorem2.3.2 Set [H, K, ,σ] be dual weak bialgebras, ifσConvolutioninvertible andεK(kl) =εK(k)εK(l), thenσ(?)1(h, kg) =σ(?)1(h(1), g)σ(?)1(h(2), k)Theorem2.3.3 Set f : H→B be weak bialgebra homomorphism, and[H₁, H₂, ,σ] be dual weak bialgebras, then f(H₁), f(H₂) be B's weak subal-gebras, and [f(H₁), f(H₂),σ] also be dual weak bialgebras.Section 3 gets some conclusions of weak Hopf modules. The main results arebelow:Definition3.1.2: Set K be H's weak Hopf algebras, M be any space, if Msatisfies:(1)(M,(?)) be right K-modules(2)(M,ρ) be right H-comodules(3)ρ: M→M (?) H be right K-module homomorphism. then M be right (H,K)-weak Hopf modules.Definition3.1.3: Set K be H's weak Hopf algebras, M be any space, if Msatisfies:(1)(M,(?)) be right H-modules(2)(M,ρ) be left K-comodules(3)ρ: M→K (?) M be right H-comodule homomorphism.then M be right (K,H)-weak Hopf modules.Theorem3.1.1 Set H be weak Hopf algebras , K be H's weak subalge-bras, and (?)K be algebra homomorphism. V be any space, then VK V (?) Kcan be right (H, K)(?) weak Hopf modules.Theorem3.2.1 Set H be weak Hopf algebras , then (H, (?)H) be H(?)'s comod-ules, and Coinv H = L(H)Theorem3.2.2 Set H be weak Hopf algebras , then K≤H. (M, (?),ρ) beweak H(?) Hopf modules. Then(1) (1 (?)εH)ρ= (?)(1 (?) HR)ρ(2) (?)m∈Coinv M we haveρ(m) = m·1(1) (?) 1(2)(3) (?)(1 (?) S)ρ(M) (?) Coinv M and Coinv M be M's right HL(?)'s modules.Theorem3.2.3 Set H be weak Hopf algebras , K be H's weak Hopf subalgebras.(M, (?),ρ)be weak (H,K)–Hopf modules. Let M = Coinv M (?) K, thenα: M (?)→M beweak (H,K)–Hopf module isomorphism.Theorem3.3.1 Set H be weak Hopf algebras , then from the examples abovewe have (H,ρ) be right Hop(?)H(?) comodules, (H, (?)) be right Hop(?)H(?) modules.Defineψ: H (?) H (?)→H (?) H then:(1)ψ(1 (?) MH) = (MH (?) 1)(1 (?)ψ)(ψ(?) 1);(2)(1 (?) (?)H)ψ= (ψ(?) 1)(1 (?)ψ)((?)H (?) 1).Keywords: weak Hopf algebras;Integrals;weak Hopf module ;Invariants;Coinvariants.