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Algebra and Discrete Mathematics, 2005, Issue 4, Pages 1–15 (Mi adm316)  

This article is cited in 4 scientific papers (total in 4 papers)

RESEARCH ARTICLE

Generators and relations for the semigroups of increasing functions on $\mathbb N$ and $\mathbb Z$

Vadym Doroshenko

Kyiv Taras Shevchenko University, Department of Mechanics and Mathematics, Volodymyrska, 60, Kyiv 01033, Ukraine
Full-text PDF (237 kB) Citations (4)
Abstract: The semigroups of all increasing functions over $\mathbb{N}$ and $\mathbb{Z}$ are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semigroups are presented in terms of generators and relations.
Keywords: Order-preserving transformation, monotonic function, generating system, generators and relations, word problem.
Received: 13.07.2005
Revised: 28.10.2005
Bibliographic databases:
Document Type: Article
MSC: 20M05, 20M20
Language: English
Citation: Vadym Doroshenko, “Generators and relations for the semigroups of increasing functions on $\mathbb N$ and $\mathbb Z$”, Algebra Discrete Math., 2005, no. 4, 1–15
Citation in format AMSBIB
\Bibitem{Dor05}
\by Vadym~Doroshenko
\paper Generators and relations for the semigroups of increasing functions on $\mathbb N$ and $\mathbb Z$
\jour Algebra Discrete Math.
\yr 2005
\issue 4
\pages 1--15
\mathnet{http://mi.mathnet.ru/adm316}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2237698}
\zmath{https://zbmath.org/?q=an:1092.20044}
Linking options:
  • https://www.mathnet.ru/eng/adm316
  • https://www.mathnet.ru/eng/adm/y2005/i4/p1
  • This publication is cited in the following 4 articles:
    1. Gutik V O. Savchuk A.S., “on Inverse Submonoids of the Monoid of Almost Monotone Injective Co-Finite Partial Selfmaps of Positive Integers”, Carpathian Math. Publ., 11:2 (2019), 296–310  crossref  mathscinet  zmath  isi  scopus
    2. Musunthia T., Koppitz J., “Maximal Subsemigroups of Some Semigroups of Order-Preserving Mappings on a Countably Infinite Set”, Forum Math., 29:4 (2017), 971–984  crossref  mathscinet  zmath  isi  scopus
    3. Oleg Gutik, Inna Pozdnyakova, “On monoids of monotone injective partial selfmaps of $L_n\times_{\operatorname{lex}}\mathbb{Z}$ with co-finite domains and images”, Algebra Discrete Math., 17:2 (2014), 256–279  mathnet  mathscinet
    4. Doroshenko V.V., “On Semigroups of Order-Preserving Transformations of Countable Linearly Ordered Sets”, Ukr. Math. J., 61:6 (2009), 859–872  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
    Statistics & downloads:
    Abstract page:167
    Full-text PDF :112
    References:5
    First page:1
     
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