On the number of subsemigroups of direct products involving the free monogenic semigroup
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The direct product ℕ x ℕ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for ℕ x S, where S is a finite semigroup. It contains only countably manypairwise non-isomorphic 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.
Clayton , A & Ruskuc , N 2019 , ' On the number of subsemigroups of direct products involving the free monogenic semigroup ' Journal of the Australian Mathematical Society , vol. First View . https://doi.org/10.1017/S1446788718000605
Journal of the Australian Mathematical Society
© 2019 Australian Mathematical Publishing Association Inc. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/S1446788718000605
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