On the number of subsemigroups of direct products involving the free monogenic semigroup
Abstract
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.
Citation
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
Publication
Journal of the Australian Mathematical Society
Status
Peer reviewed
ISSN
1446-7887Type
Journal article
Collections
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