1 results
ON THE NUMBER OF SUBSEMIGROUPS OF DIRECT PRODUCTS INVOLVING THE FREE MONOGENIC SEMIGROUP
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society / Volume 109 / Issue 1 / August 2020
- Published online by Cambridge University Press:
- 01 February 2019, pp. 24-35
- Print publication:
- August 2020
-
- Article
- Export citation
-
The direct product
$\mathbb{N}\times \mathbb{N}$ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for 
$\mathbb{N}\times S$, 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.
