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Abstract.This paper describes a constructive method of finding all congruences p on commutative cancellative archimedean semigroups 5 without idempotents (A'-semigroups) such that Sip is noncancellative and without idempotents. These congruences are refinements of ^-congruences : a congruence r¡ is an N-congruence if S¡r¡ is an N-semigroup.
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