This paper describes a constructive method of finding all congruences ρ on commutative cancellative archimedean semigroups S without idempotents (N-semigroups) such that S/ρ is noncancellative and ...

Let S be a regular semigroup and let ρ be a congruence relation on S. The kernel of ρ, in notation $\ker \rho$, is the union of the idempotent ρ-classes. The trace of ρ, in notation tr ρ, is the ...