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Notes on Partially Ordered Monoids
LIU Pengyuan 1,YANG Yichuan 1 *,MUHAMMAD Zafrullah 2
1.Department of Mathematics and System Sciences, LMIB of theMinistry of Education, Beijing University of Aeronautics andAstronautics, 100191 Beijing, China
2.Department of Mathematics, University of Iowa, IA 52242 Iowa City, USA
*Correspondence author
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Funding: Supported by the NSFC (Grant 11271040) and the Fundamental Research Funds for the Central Universities （No.YWF-14-SXXY-015）
Opened online: 3 December 2014
Accepted by: none
Citation: LIU Pengyuan,YANG Yichuan,MUHAMMAD Zafrullah.Notes on Partially Ordered Monoids[OL]. [ 3 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4620489
 
 
In this paper, we give the definitions of positive elements, positive cones and pri-\mal elements of partially ordered monoids. Then we consider the Riesz interpolation property of partially ordered monoids, and thus we introduce the definition of the weak Riesz interpola-\tion property of partially ordered monoids. At the same time, we consider the (pR) condition in the partially ordered groups just like in partially ordered groups, and generalize the (pR) c-\ondition to (WpR) condition. On the basis of these, we consider the Conrad's F-condition for lattice-ordered monoids, Riesz monoids, and pre-Riesz monoids.
Keywords:Lattice-ordered monoid, Riesz monoid, Pre-Riesz monoid, F-condition, Homogeneous element, Basis
 
 
 

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