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

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
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
\Bibitem{Tes97} \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 \mathnet{http://mi.mathnet.ru/mz1680} \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} 

• http://mi.mathnet.ru/eng/mz1680
• https://doi.org/10.4213/mzm1680
• http://mi.mathnet.ru/eng/mz/v62/i6/p910

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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
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