The research unit Algebra develops research on ring theory, groups and semigroups. This includes research on the algebraic structure of important classes of rings and semigroups, such as, group and semigroup rings, lineair groups and submonoids of polycyclic-by-finite groups. The main goals include the description of the unit group of integral group rings, the isomorphism problem of group rings, the characterisation of Noetherian semigroup algebras, the determination of prime ideals of such algebras and also to determine when these are maximal orders.