Abstract
This article mainly gives the structure theorem of weak comodule algebras, that is, assume that H is a weak Hopf algebra, and B a weak right H-comodule algebra, if there exists a morphism φ: H → B of a weak right H-comodule algebras, then there exists an algebra isomorphism: B ≅ B coH #H, where B coH denotes the coinvariant subalgebra of B, and B coH #H denotes the weak smash product.
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