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Clayton, Ashley, Reilly, Catherine 
ORCID: https://orcid.org/0009-0001-5079-2136 and Ruškuc, Nik
(2025)
On the number of subdirect products involving semigroups of integers and natural numbers.
Journal of Algebra and Its Applications.
ISSN 0219-4988
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Abstract
In this paper, we extend a recent result that for the (additive) semigroup of positive integers ℕ, there are continuum many subdirect products of ℕ × ℕ up to isomorphism. We prove that for U,V each one of ℤ (the group of integers), ℕ 0 (the monoid of non-negative integers), or ℕ, the direct product U × V contains continuum many (semigroup) subdirect products up to isomorphism.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | semigroup,indecomposable element,integer,natural number,subdirect product,applied mathematics,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2604 |
| Faculty \ School: | Faculty of Science Faculty of Science > School of Engineering, Mathematics and Physics |
| UEA Research Groups: | Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR) |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 11 Jan 2025 01:03 |
| Last Modified: | 18 Jun 2026 20:30 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/98172 |
| DOI: | 10.1142/S0219498826501379 |
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