Graph products of residually finite monoids are residually finite

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.

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Bibliographic Details
Published inJournal of algebra Vol. 662; pp. 514 - 527
Main Authors Cho, Jung Won, Gould, Victoria, Ruškuc, Nik, Yang, Dandan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2025
Subjects
Free products
Graph products
Monoids
Residual finiteness
20M10
20M05
Residual finiteness
Free products
Monoids
Graph products
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Summary: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.
ISSN:0021-8693
DOI:10.1016/j.jalgebra.2024.07.057