Notes on Partially Ordered Monoids
首发时间:2014-12-03
Abstract: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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偏序幺半群的一些研究
摘要:在这篇文章中,我们给出了偏序幺半群中正元、正锥以及原始元的定义。接着,我们考虑了偏序幺半群上的Riesz interpolation性质,并且我们进一步给出了偏序幺半群上的弱Riesz interpolation性质。与此同时,正如偏序群中的讨论一样,我们也考虑了偏序幺半群上的(pR)\条件,并将(pR)条件推广为(WpR)条件。在此基础上,我们考虑了格序幺半群、Riesz幺半群和pre-Riesz幺半群上的Conrad F-条件和基之间的关系。
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