An algebraic approach to BP∗(BZ/pk)

For a prime p let BP be the Brown–Peterson spectrum with homotopy ring BP∗=Z(p)[v1,v2,v3,…]. Using the arithmetical properties of the coefficients in the Brown–Peterson pk-series, we obtain the complete structure of the Z(p)[v2,v3,…]-module generated by the canonical elements di∈BP2i−1(BZ/pk).