Modules
Magma handles finitely generated modules over Noetherian rings, including submodule lattices, composition series, and homomorphism spaces. Modules over group algebras connect directly to representation theory.
Contributors
Homological Algebra
The packages for chain complexes and basic algebras have been developed by Jon Carlson (Athens, GA).
Sergei Haller developed Magma code for computing the first cohomology group of a finite group with coefficients in a finite (not necessarily abelian) group. This formed the basis of a package for computing Galois cohomology of linear algebra groups.
Machinery for computing group cohomology and for producing group extensions has been developed by Derek Holt (Warwick). There are two parts to this machinery. The first part comprises Derek's older C-language package for permutation groups while the second part comprises a recent Magma language package for group cohomology.
In 2011, Derek Holt (Warwick) implemented an alternative algorithm for finding the dimension of the cohomology group Hn(G,K), for G a finite group, and K a finite field. In this approach the dimension is found using projective covers and dimension shifting.
The code for computing A∞-structures in group cohomology was developed by Mikael Vejdemo Johansson (Jena).