| In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators. |
| After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg. |
| He lectured on and wrote up notes on Tate's theorem on homomorphisms between abelian varieties over finite fields. |
| He does provide an example of the decomposition of an abelian group into cosets of a subgroup. |
| His results on this topic provided connections between number theory, theta functions, and the transformations of abelian functions. |
| Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals. |
