Cancellative and archimedean Ideal-extensions by commutative semigroups.
We describe algorithms for computing the nilradical and the zero-divisors of a finitely generated commutative -monoid. These algorithms will be used for deciding if a given ideal of a finitely generated commutative -monoid is prime, radical or primary.
Every commutative nil-semigroup of index 2 can be imbedded into such a semigroup without irreducible elements.