标题： 剩余格中的共极大滤子图 显示英文标题

标题： Comaximal filter graphs in residuated lattices

摘要： 考虑A为一个交换的、积分的且非退化的剩余格。 在这项工作中，我们引入了剩余格A上余极大滤子图。 我们将用Cf(A)表示这个图，其顶点集是A中不是包含在A的根中的适当滤子，并且顶点间的邻接关系定义为：考虑两个滤子F和G，它们相邻当且仅当F v G生成的滤子等于A。 我们提供了该图的一些基本性质，并建立了这种余极大滤子图与零因子图之间的联系。 此外，我们研究了图Cf(A)的色数、团数、平面性和完美性。 我们还简要描述了在特定小规模剩余格上构造的所有余极大滤子图。 显示英文摘要

摘要： Consider A to be a commutative, integral and non-degenerate residuated lattice. In this work, we introduce the graph of comaximal filters on the residuated lattice A. We willdenote by Cf(A) this graph for which the set of vertices are proper filters of A which are not contained in the radical of A, and the adjacency relation on vertices is given as: consider two filters F and G, there are adjacent if and only if F v G; the filter generated by F u G is equal to A. The elementary properties of this graph are provided, we establish a link between this comaximal filter graphs and the zero-divisor graphs. Furthermore, we investigate the chromatic number, the clique number, the planarity and the perfection of the graph Cf(A). We also briefly describe all the comaximal filter graphs constructed on specific residuated lattices of small size.