酉格序阿贝尔群的单纯几何
Simplicial geometry of unital lattice-ordered abelian groups
摘要：
所谓$\ell$ -群$G$，我们是指格序阿贝尔群。本文研究了由{ \it unital} $\ell$ -群构成的范畴$\FP$，这些$\ell$ -群具有一个特殊的序单位$u$ .利用$\FP$与有理多面体范畴之间的对偶性，我们将给出（i）$\FP$中有限极限和余极限的构造;（ii）关于可表示有单位$\ell$ -群的Cantor-Bernstein-Schröder定理;（iii）$\FP$的自由对象的可表示生成子代数的几何刻画.
英文摘要：
By an $\ell$-group $G$ we mean a lattice-ordered abelian group. This paper is concerned with the category $\FP$ of finitely presented {\it unital} $\ell$-groups, those $\ell$-groups having a distinguished order-unit $u$. Using the duality between $\FP$ the category of rational polyhedra, we will provide (i) a construction of finite limits and co-limits in $\FP$; (ii) a Cantor-Bernstein-Schröder theorem for finitely presented unital $\ell$-groups; (iii) a geometrical characterization of finitely generated subalgebras of free objects of $\FP$.
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