| Herbrand also worked on field theory considering abelian extensions of algebraic number fields. |
| He lectured on and wrote up notes on Tate's theorem on homomorphisms between abelian varieties over finite fields. |
| In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators. |
| In his talk Steinitz introduced an algebra over the ring of integers whose base elements are isomorphism classes of finite abelian groups. |
| Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals. |
| Schreier showed that the fundamental group of such a space is always abelian. |
