We introduce a class of finite semigroups obtained by considering Rees

quotients of numerical semigroups.

Several natural questions concerning this class, as well as particular

subclasses obtained by considering some special ideals, are answered while

others remain open. We exhibit nice presentations for these semigroups and

prove that the Rees quotients by ideals of N, the positive integers under

addition, constitute a set of generators for the pseudovariety of commutative

and nilpotent semigroups.

DOI: 10.4171/PM/1927