  We present an algebraic investigation of generalized and equiaffine curvature
tensors in a given pseudo-Euclidean vector space and study different
orthogonal, irreducible decompositions in analogy to the known decomposition of
algebraic curvature tensors. We apply the decomposition results to characterize
geometric properties of Codazzi structures and relative hypersurfaces;
particular emphasis is on projectively flat structures.
