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

Ashley Clayton; Catherine Reilly; Nik Ruškuc

doi:10.1142/S0219498826501379

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

Ashley Clayton, Catherine Reilly, Nik Ruškuc

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	2650137
Journal	Journal of Algebra and Its Applications
Early online date	18 Feb 2025
DOIs	https://doi.org/10.1142/S0219498826501379
Publication status	E-pub ahead of print - 18 Feb 2025

Keywords

Semigroup
indecomposable element
integer
natural number
subdirect product

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10.1142/S0219498826501379

subdirectproductsofZxZ 19Accepted author manuscript, 328 KB

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

Abstract

Keywords

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