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On The Number Of Subsemigroups Of Direct Products Involving The Free Monogenic Semigroup
The direct product N×N of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for N×S , where S is a finite semigroup. It contains only countably many pairwise nonisomorphic subsemigroups if and only if S is a union of groups. And it contains only countably many pairwise nonisomorphic subdirect products if and only if every element of S has a relative left or right identity element.
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