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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 910–915 (Mi mz1680)  

This article is cited in 1 scientific paper (total in 1 paper)

An analog of the fundamental theorem of arithmetic in ordered groupoids

V. A. Testov

Vologda State Pedagogical University

Abstract: In the note we consider ordered groupoids with the Riesz interpolation property, that is, if $a_i\le b_j$ ($i,j=1,2$), then there exists a $c$ such that $a_i\le c\le b_j$ ($i,j=1,2$). For such groupoids possessing the descending chain condition for the positive cone and the property
$$ \forall a,b \quad a\le b \implies\exists u,v \quad au=va=b, $$
a theorem analogous to the fundamental theorem of arithmetic is proved. The result is a generalization of known results for lattice-ordered monoids, loops, and quasigroups.

DOI: https://doi.org/10.4213/mzm1680

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English version:
Mathematical Notes, 1997, 62:6, 762–766

Bibliographic databases:

UDC: 512.548.4
Received: 10.04.1995
Revised: 05.11.1996

Citation: V. A. Testov, “An analog of the fundamental theorem of arithmetic in ordered groupoids”, Mat. Zametki, 62:6 (1997), 910–915; Math. Notes, 62:6 (1997), 762–766

Citation in format AMSBIB
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\by V.~A.~Testov
\paper An analog of the fundamental theorem of arithmetic in ordered groupoids
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 6
\pages 910--915
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\crossref{https://doi.org/10.4213/mzm1680}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1635186}
\zmath{https://zbmath.org/?q=an:0926.06007}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 762--766
\crossref{https://doi.org/10.1007/BF02355465}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075396200031}


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    This publication is cited in the following articles:
    1. Brauner N., Gravier S., Kronek L.-Ph., Meunier F., “Lad Models, Trees, and an Analog of the Fundamental Theorem of Arithmetic”, Discrete Appl. Math., 161:7-8 (2013), 909–920  crossref  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
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