On simultaneously nilpotent antiring matrices

Antirings are an important type of semirings, which generalize Boolean algebra, fuzzy algebra, distributive lattice and incline. In this paper, we study the issue of nilpotent antiring matrices, provide some properties and characterizations of the simultaneous nilpotence for a finite number of antiring matrices, present some methods for calculating the simultaneously nilpotent index of a finite number of antiring matrices. Partial results obtained in this paper generalize and develop the corresponding ones on nilpotent antiring matrices and on simultaneously nilpotent fuzzy matrices (lattice matrices).