Noncancellative congruences on $N$-semigroups
Robert P. Dickinson · Proceedings of the American Mathematical Society · 1972
This paper describes a constructive method of finding all congruences $\rho$ on commutative cancellative archimedean semigroups S without idempotents (N-semigroups) such that $S/\rho$ is noncancellative and without idempotents. These congruences are refinements of N-congruences; a congruence $\eta$ is an N-congruence if $S/\eta$ is an N-semigroup.