Springer Nature 1998 paper vector sublattice sublattice https://scigraph.springernature.com/explorer/license/ cone positive elements en positive cone 1998-01-01 https://doi.org/10.1007/978-3-642-72222-6_7 Finitely Generated Vector Sublattices 2022-01-01T19:17 false arbitrary elements elements Let E+ be the positive cone of an Archimedean vector lattice E. It is shown in [4, Theorem 2.1] that for arbitrary u, v ∈ E+ the vector sublattice R(u, v) of E generated by u and v can be described as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R\left( {u,\upsilon } \right) = Span\left\{ {{{{\left( {\alpha u + \beta \upsilon } \right)}}^{ + }}:\alpha \beta \in \mathbb{R}} \right\}.$$\end{document}.We will demonstrate in this paper that this result no longer holds for three or more positive elements. It also ceases to be true for the vector sublattice generated by two (or more) arbitrary elements. Moreover, we will show that every finitely generated vector sublattice of E is finite-dimensional if and only if E is hyper-Archimedean. chapter e. 79-95 Archimedean vector lattice E. chapters vector lattice E. lattice E. results Charles B. Huijsmans Avgerinos Evgenios Yannelis Nicholas C. Springer Nature - SN SciGraph project pub.1019422947 dimensions_id 978-3-642-72224-0 978-3-642-72222-6 Functional Analysis and Economic Theory Medical and Health Sciences Yuri Abramovich Department of Mathematics, Leiden University, The Netherlands Department of Mathematics, Leiden University, The Netherlands Neurosciences 10.1007/978-3-642-72222-6_7 doi