e-Idempotent Matrices over Commutative Semirings

In this work, we introduce the notion of -idempotent matrices over a commutative semiring, this is a generalization of the idempotent matrices. We investigate some characteristic properties of -idempotent matrices over general semirings. We provide a formula to calculate the number of -idempotent triangular matrices over finite commutative semirings without zero divisors.