2025/05/05 by Surdive Atamewoue, Atamewoue, Surdive, Hugue Tchantcho +1
Computer Science · #Advanced Algebra and Logic #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2505.02399
openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.