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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2010, том 9, выпуск 1, страницы 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

Аннотация: 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.

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

MSC: 20M05, 20F65

Поступила в редакцию: 24.11.2009
Исправленный вариант: 15.05.2010

Язык публикации: английский



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