The Chow rings of generalized Grassmannians

Based on the Basis theorem of Bruhat–Chevalley [C] and the formula for multiplying Schubert classes obtained in [D\QTR{group}{u}] and programed in [DZ${}_{\text{QTR}group1}$], we introduce a new method computing the Chow rings of flag varieties (resp. the integral cohomology of homogeneous spaces). The method and results of this paper have been extended in [DZ${}_3$, DZ${}_4$] to obtain the integral cohomology rings of all complete flag manifolds, and to construct the integral cohomologies of Lie groups in terms of Schubert classes.