On nilpotent matrices over antirings

In this paper, the nilpotent matrices over commutative antirings are characterized in terms of principal permanental minors, main diagonals and permanental adjoint matrices, and a necessary and sufficient condition for a nilpotent matrix over a commutative antiring which has a given nilpotent index is obtained. Also, a method for calculating the nilpotent index of any nilpotent matrix over a commutative entire antiring is given.