Length functions for semigroup embeddings

• Date: 2018
• Main Author: Davis, Tara Colleen
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Membership problem; Word problem; Embeddings of Semigroups; Length Function; Distortion; 20M05; 20F65
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/618
• Journal Title: Algebra and Discrete Mathematics

Following the work done in [O] for groups, we describe, for a given semigroup \(S\), which functions \(l : S \to \mathbb{N} \) can be realized up to equivalence as length functions \(g\mapsto |g|_H\) by embedding S into a finitely generated semigroup \(H\). We also, following the work done in [O2] a...