标题： 粘合剩余格 显示英文标题

标题： Gluing residuated lattices

摘要： 我们引入并刻画了剩余格的各种粘合构造，这些构造在公共子重积上相交，并且是所得结构的子代数或适当的子重积。从1-求和构造（也称为剩余结构的序和）开始，其中仅在最大元相交的代数被粘合在一起，我们首先考虑基于同余滤子的粘合，然后进一步加入一个格理想。 我们用（可能为部分的）算子作用于（可能为部分的）剩余结构来刻画这类构造。作为粘合构造的具体例子，我们得到了一些旋转构造的非交换版本，以及一种有趣的半线性剩余格，它们是2幂零的。这项研究还试图通过在特殊情况下构建一个互可组合物（当V型结构中的公共子代数要么是一个特殊的（同余）滤子，要么是滤子与理想的并集时），为非交换剩余格的互可组合性研究迈出第一步。 显示英文摘要

摘要： We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction (also known as ordinal sum for residuated structures), where algebras that intersect only in the top element are glued together, we first consider the gluing on a congruence filter, and then add a lattice ideal as well. We characterize such constructions in terms of (possibly partial) operators acting on (possibly partial) residuated structures. As particular examples of gluing constructions, we obtain the non-commutative version of some rotation constructions, and an interesting variety of semilinear residuated lattices that are 2-potent. This study also serves as a first attempt toward the study of amalgamation of non-commutative residuated lattices, by constructing an amalgam in the special case where the common subalgebra in the V-formation is either a special (congruence) filter or the union of a filter and an ideal.