Graph products of residually finite monoids are residually finite

Jung Won Cho; Victoria Gould; Nik Ruskuc; Dandan Yang

doi:10.1016/j.jalgebra.2024.07.057

Graph products of residually finite monoids are residually finite

Jung Won Cho^*, Victoria Gould^*, Nik Ruskuc^*, Dandan Yang^*

^*Corresponding author for this work

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

Abstract

We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of semigroups follow.

Original language	English
Pages (from-to)	514-527
Journal	Journal of Algebra
Volume	662
Early online date	9 Sept 2024
DOIs	https://doi.org/10.1016/j.jalgebra.2024.07.057
Publication status	Published - 15 Jan 2025

Keywords

Monoids
Free products
Graph products
Residual finiteness

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10.1016/j.jalgebra.2024.07.057

Cho-2024-Graph-products-of-JAlgebra-662-514-AAM-CCBY
Copyright © 2024 the Authors. This work has been made available online in accordance with the University of St Andrews Open Access policy. This accepted manuscript is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2024.07.057.
Accepted author manuscript, 331 KBLicence: CC BY

Cite this

@article{2b46d13c8c9045a8a6c61844b75628f6,

title = "Graph products of residually finite monoids are residually finite",

abstract = "We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of semigroups follow.",

keywords = "Monoids, Free products, Graph products, Residual finiteness",

author = "Cho, {Jung Won} and Victoria Gould and Nik Ruskuc and Dandan Yang",

note = "Funding: The second author is supported by the Engineering and Physical Sciences Research Council Grant EP/V002953/1. The third author is supported by the Engineering and Physical Sciences Research Council Grant EP/V003224/1. The fourth author is supported by the National Natural Science Foundation of China Grant No. 12171380, the Natural Science Basic Research Program of Shaanxi Province Grant No. 2023-JC-JQ-04, and the Shaanxi Fundamental Science Research Project for Mathematics and Physics Grant No. 22JSQ034.",

year = "2025",

month = jan,

day = "15",

doi = "10.1016/j.jalgebra.2024.07.057",

language = "English",

volume = "662",

pages = "514--527",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press/Elsevier ",

}

TY - JOUR

T1 - Graph products of residually finite monoids are residually finite

AU - Cho, Jung Won

AU - Gould, Victoria

AU - Ruskuc, Nik

AU - Yang, Dandan

N1 - Funding: The second author is supported by the Engineering and Physical Sciences Research Council Grant EP/V002953/1. The third author is supported by the Engineering and Physical Sciences Research Council Grant EP/V003224/1. The fourth author is supported by the National Natural Science Foundation of China Grant No. 12171380, the Natural Science Basic Research Program of Shaanxi Province Grant No. 2023-JC-JQ-04, and the Shaanxi Fundamental Science Research Project for Mathematics and Physics Grant No. 22JSQ034.

PY - 2025/1/15

Y1 - 2025/1/15

N2 - We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of semigroups follow.

AB - We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of semigroups follow.

KW - Monoids

KW - Free products

KW - Graph products

KW - Residual finiteness

UR - https://arxiv.org/abs/2403.13614

U2 - 10.1016/j.jalgebra.2024.07.057

DO - 10.1016/j.jalgebra.2024.07.057

M3 - Article

SN - 0021-8693

VL - 662

SP - 514

EP - 527

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Graph products of residually finite monoids are residually finite

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Right Noetherian and coherent monoids: Right Noetherian and coherent monoids

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Graph products of residually finite monoids are residually finite

Abstract

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