On the number of subdirect products involving semigroups of integers and natural numbers

Clayton, Ashley, Reilly, Catherine 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:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	11 Jan 2025 01:03
Last Modified:	11 Oct 2025 11:34
URI:	https://ueaeprints.uea.ac.uk/id/eprint/98172
DOI:	10.1142/S0219498826501379

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