On the isomorphism problem for commutative semigroups

We give some statements on the structure of finitely generated commutative semigroups which permit us to find necessary and sufficient conditions of isomorphism of two finitely presented commutative semigroups. This part of the article might be of independent interest. However, the main result for us is the recursive equivalence of the following three algorithmic problems: the isomorphism problem for commutative semigroups, the isomorphism problem for regular commutative semigroups and the conjugacy problem for finite sequences of elements in the groups $GL(l,Z)$.
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