标题： 公理化周期 l-前群的小种类 显示英文标题

标题： Axiomatizing small varieties of periodic l-pregroups

摘要： 我们为由$n$-周期 l-预群$\mathbf{F}_n(\mathbb{Z})$生成的种类提供公理化，对于每个$n \in \mathbb{Z}^+$以及所有可能的此类种类的并集；有限并集在 l-预群的子种类格中形成一个理想，并且我们完全描述了其格结构。 在此过程中，我们将由$\mathbf{F}_n(\mathbb{Z})$生成的种类中的所有有限次直接不可约（FSI）代数表征为具有全序群骨架（并且不是平凡的）的$n$-周期 l-预群。 那些不是 l-群的有限生成的 FSI 进一步表征为一个（有限生成的）全序阿贝尔 l-群与$\mathbf{F}_k(\mathbb{Z})$的字典积，其中$k \mid n$。 显示英文摘要

摘要： We provide an axiomatization for the variety generated by the $n$-periodic l-pregroup $\mathbf{F}_n(\mathbb{Z})$, for every $n \in \mathbb{Z}^+$, as well as for all possible joins of such varieties; the finite joins form an ideal in the subvariety lattice of l-pregroups and we describe fully its lattice structure. On the way, we characterize all finitely subdirectly irreducible (FSI) algebras in the variety generated by $\mathbf{F}_n(\mathbb{Z})$ as the $n$-periodic l-pregroups that have a totally ordered group skeleton (and are not trivial). The finitely generated FSIs that are not l-groups are further characterized as lexicographic products of a (finitely generated) totally ordered abelian l-group and $\mathbf{F}_k(\mathbb{Z})$, where $k \mid n$.