This article is cited 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.

UDC: 512.548.4

Received: 10.04.1995
Revised: 05.11.1996

DOI: 10.4213/mzm1680

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

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