Invertible and nilpotent matrices over antirings

AbstractIn this paper, we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GLn(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of ⌈log2n⌉ square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum