分配格上的Cevian运算
Cevian operations on distributive lattices
摘要：
我们构造了一个完全正规有界分配格D，其中对于每对元素（a，b），集合{x $\in$ D| a $\le$ b $\lor$ x}具有可计数的共初始子集，使得D不携带任何二元运算-满足恒等式x $\le$ y $\lor$（x-y），（x-y）$\land$（y-x）= 0和x-z $\le$（x-y）$\lor$（y-z）。特别地，D不是任何（不一定是阿贝尔的）{ \ell }-群的所有凸生成的{\ell }-子群的格的同态像。它有$\aleph 2 elements. This solves negatively a few problems stated by Iberkleid, Mart{í}nez, and McGovern in 2011 and recently by the author. This work also serves as preparation for a forthcoming paper in which we prove that for any infinite cardinal $ λ $, the class of Stone duals of spectra of all Abelian {\ell}-groups with order-unit is not closed under L $ \infty $ $λ$ -初等等价。
英文摘要：
We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x $\in$ D | a $\le$ b $\lor$ x} has a countable coinitial subset, such that D does not carry any binary operation - satisfying the identities x $\le$ y $\lor$(x-y),(x-y)$\land$(y-x) = 0, and x-z $\le$ (x-y)$\lor$(y-z). In particular, D is not a homomorphic image of the lattice of all finitely generated convex {\ell}-subgroups of any (not necessarily Abelian) {\ell}-group. It has $\aleph 2 elements. This solves negatively a few problems stated by Iberkleid, Mart{í}nez, and McGovern in 2011 and recently by the author. This work also serves as preparation for a forthcoming paper in which we prove that for any infinite cardinal $λ$, the class of Stone duals of spectra of all Abelian {\ell}-groups with order-unit is not closed under L $\infty$$λ$-elementary equivalence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
