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We study the structure of the 0-Schur algebra S0(n,r)S0(n,r) following the geometric construction of S0(n,r)S0(n,r) by Jensen and Su . The main results are the construction and classification of indecomposable projective modules. In addition, we construct bases of these modules and their homomorphism spaces. We also give a filtration of projective modules, which leads to a decomposition of S0(n,r)S0(n,r) into indecomposable left modules.