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Algebra Discrete Math., 2010, Volume 9, Issue 1, Pages 1–15 (Mi adm17)  

RESEARCH ARTICLE

Length functions for semigroup embeddings

Tara Colleen Davis

Department of Mathematics 1326 Stevenson Center Vanderbilt University Nashville, TN 37240 USA

Abstract: Following the work done in $[\mathrm O]$ for groups, we describe, for a given semigroup $S$, which functions $l\colon S\to\mathbb{N}$ 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 $[\mathrm O_2]$ and $[\mathrm{OS}]$, provide a complete description of length functions of a given finitely generated semigroup with enumerable set of relations inside a finitely presented semigroup.

Keywords: Membership problem, word problem, embeddings of semigroups, length function, distortion.

Full text: PDF file (255 kB)

Bibliographic databases:
MSC: 20M05, 20F65
Received: 24.11.2009
Revised: 15.05.2010
Language:

Citation: Tara Colleen Davis, “Length functions for semigroup embeddings”, Algebra Discrete Math., 9:1 (2010), 1–15

Citation in format AMSBIB
\Bibitem{Dav10}
\by Tara Colleen Davis
\paper Length functions for semigroup embeddings
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 1
\pages 1--15
\mathnet{http://mi.mathnet.ru/adm17}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2676708}
\zmath{https://zbmath.org/?q=an:1209.20048}


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