ABSTRACT
The class of FC-groups, that is, groups any element of which has finitely many conjugates, plays an important role in the theory of group algebras. Among other things, it provides an effective technique (called Δ-methods) for studying this class of algebras and yields a description of the center and of prime and semiprime group algebras. This chapter presents an analog of the FC-center of a group in the case of an arbitrary cancellative semigroup. It establish some fundamental properties of Δ-methods. To improve the information on an arbitrary cancellative semigroup, it may seem reasonable to consider some other FC-groups associated with the ancellative semigroup.
