ON THE NUMBER OF SUBSEMIGROUPS OF DIRECT PRODUCTS INVOLVING THE FREE MONOGENIC SEMIGROUP
| Autor: | Nik Ruskuc, Ashley Clayton |
|---|---|
| Přispěvatelé: | University of St Andrews. Pure Mathematics, University of St Andrews. School of Mathematics and Statistics, University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Mathematics::Operator Algebras 010505 oceanography Semigroup General Mathematics Mathematics::Rings and Algebras T-NDAS 010102 general mathematics Mathematics::General Topology Subsemigroup 01 natural sciences Subdirect product Mathematics::Logic Free mongenic semigroup Pairwise comparison QA Mathematics 0101 mathematics Identity element Element (category theory) QA Direct product 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Journal of the Australian Mathematical Society. 109:24-35 |
| ISSN: | 1446-8107 1446-7887 |
| DOI: | 10.1017/s1446788718000605 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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