On -operators in an arbitrary semigroup
A necessary and sufficient condition is given for a) a principal left ideal in to be equal to the direct product of the corresponding principal left ideals , b) an -class to be equal to the direct product of the corresponding -classes .
We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.