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Algebra i logika, 2012, Volume 51, Number 5, Pages 652–667 (Mi al556)  
This article is cited in 5 scientific papers (total in 5 papers)

Finitely presented expansions of computably enumerable semigroups

D. R. Hirschfeldta, B. Khoussainovb

a Department of Mathematics, University of Chicago, Chicago, IL, USA
b Department of Computer Science, University of Auckland, Auckland, New Zealand
Full-text PDF (209 kB) Citations (5)
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Abstract: Every computable universal algebra has a finitely presented expansion. On the other hand, there are examples of finitely generated, computably enumerable universal algebras with no finitely presented expansions. It is natural to ask whether such examples can be found in well-known classes of algebras such as groups and semigroups. Here we build an example of a finitely generated, infinite, computably enumerable semigroup with no finitely presented expansions.We also discuss other interesting computability-theoretic properties of this semigroup.
Keywords: computably enumerable semigroup, finitely presented expansion.
Received: 16.12.2011
English version:
Algebra and Logic, 2012, Volume 51, Issue 5, Pages 435–444
DOI: https://doi.org/10.1007/s10469-012-9203-8
Bibliographic databases:
Document Type: Article
UDC: 510.53+512.53
Language: Russian
Citation: D. R. Hirschfeldt, B. Khoussainov, “Finitely presented expansions of computably enumerable semigroups”, Algebra Logika, 51:5 (2012), 652–667; Algebra and Logic, 51:5 (2012), 435–444
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
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