Let be a semiring, let be the set of matrices over . A linear operator on is said to be strongly -potent preserving if if and only if . These operators form a semigroup . In this paper we have .
If is the 2-element Boolean algebra then is generated by the transposition and the similarity operators , a permutation matrix.
If is antinegative (i.e. no element has an additive inverse) and free of zero divisors then is generated by the transposition, the similarity operators and those operators that are contained in ( denotes the Hadamard product). If moreover each element of is idempotent then such operators occur only for .