论文标题
自由矢量晶格和自由矢量晶格代数
Free vector lattices and free vector lattice algebras
论文作者
论文摘要
我们展示了如何从通用代数中的方程类别的定理得出各种自由向量晶格和自由向量晶格代数。在主要问题似乎开放的情况下，就对非空套的免费$ f $ - 代数进行了讨论。可以使用自由向量晶格和矢量晶格代数的存在结果用于简单证明存在的banach晶格和自由Banach晶格代数的结果。包括通用代数的必要材料的详细说明。
We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in universal algebra. A discussion about free $f$-algebras over non-empty sets is given, where the main issues appear to be open. It is indicated how the existence results for free vector lattices and vector lattice algebras can be used for easy proofs of existence results for free Banach lattices and free Banach lattice algebras. A detailed exposition of the necessary material from universal algebra is included.
