In this article, the comodule structure of Chow rings of Flag manifolds CH(G/B) is described by Schubert cells. Its equivariant version gives rise to a Hopf structure of the equivariant cohomology of flag manifolds H * B (G/B). We get two identities of generalized Schubert polynomials as explanations of the geometric facts.

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If this article, an elementary kernel-cokernel exact sequence is introduced for A f → B g → C. Some relative sequences and applications are discussed. This result can simplify some proofs-the indices of Frodholm operators, Harada and Sai theorem, and the derived couples of exact couples.