Loading [MathJax]/jax/output/SVG/config.js
Algebra i logika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Algebra Logika:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Algebra i logika, 2012, Volume 51, Number 5, Pages 652–667 (Mi al556)  
This article is cited in 6 scientific papers (total in 6 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 (6)
References:
PDF
HTML
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
\Bibitem{HirKho12}
\by D.~R.~Hirschfeldt, B.~Khoussainov
\paper Finitely presented expansions of computably enumerable semigroups
\jour Algebra Logika
\yr 2012
\vol 51
\issue 5
\pages 652--667
\mathnet{http://mi.mathnet.ru/al556}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3075105}
\zmath{https://zbmath.org/?q=an:06138169}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 5
\pages 435--444
\crossref{https://doi.org/10.1007/s10469-012-9203-8}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000312401000006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871388231}
Linking options:
  • https://www.mathnet.ru/eng/al556
  • https://www.mathnet.ru/eng/al/v51/i5/p652
    • This publication is cited in the following 6 articles:
    1. Huishan Wu, “Computably Enumerable Semisimple Rings”, Mathematics, 13:3 (2025), 337  crossref
    2. Nadim Kasymov, Nadira Karimova, Bakh Khoussainov, Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science, 2024, 1  crossref
    3. Valentino Delle Rose, Luca San Mauro, Andrea Sorbi, “Classifying word problems of finitely generated algebras via computable reducibility”, Int. J. Algebra Comput., 33:04 (2023), 751  crossref
    4. Bakh Khoussainov, Lecture Notes in Computer Science, 10936, Sailing Routes in the World of Computation, 2018, 1  crossref
    5. G. Wu, H. Wu, “Degrees of word problem for algebras without finitely presented expansions”, Theory and Applications of Models of Computation, TAMC 2017, Lecture Notes in Computer Science, 10185, eds. T. Gopal, G. Jager, S. Steila, Springler, 2017, 642–652  crossref  mathscinet  isi  scopus
    6. A. Gavryushkin, B. Khoussainov, F. Stephan, “Reducibilities among equivalence relations induced by recursively enumerable structures”, Theor. Comput. Sci., 612 (2016), 137–152  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
    Statistics & downloads:
    Abstract page:273
    Full-text PDF :73
    References:60
    First page:8
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025