On the number of subdirect products involving semigroups of integers and natural numbers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915093085683712 |
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| author | Clayton, Ashley Reilly, Katie Ruskuc, Nik |
| author_facet | Clayton, Ashley Reilly, Katie Ruskuc, Nik |
| contents | We extend a recent result that for the (additive) semigroup of positive integers $\mathbb{N}$, there are continuum many subdirect products of $\mathbb{N} \times \mathbb{N}$ up to isomorphism. We prove that for $U,V$ each one of $\mathbb{Z}$ (the group of integers), $\mathbb{N}_{0}$ (the monoid of non-negative integers), or $\mathbb{N}$, we prove that $U \times V$ has continuum many (semigroup) subdirect products up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04994 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the number of subdirect products involving semigroups of integers and natural numbers Clayton, Ashley Reilly, Katie Ruskuc, Nik Group Theory Combinatorics Rings and Algebras 20M13, 20M14 We extend a recent result that for the (additive) semigroup of positive integers $\mathbb{N}$, there are continuum many subdirect products of $\mathbb{N} \times \mathbb{N}$ up to isomorphism. We prove that for $U,V$ each one of $\mathbb{Z}$ (the group of integers), $\mathbb{N}_{0}$ (the monoid of non-negative integers), or $\mathbb{N}$, we prove that $U \times V$ has continuum many (semigroup) subdirect products up to isomorphism. |
| title | On the number of subdirect products involving semigroups of integers and natural numbers |
| topic | Group Theory Combinatorics Rings and Algebras 20M13, 20M14 |
| url | https://arxiv.org/abs/2311.04994 |