  Let $R$ be a commutative additively idempotent semiring. In this paper, some
properties and characterizations for permanents of matrices over $R$ are
established, and several inequalities for permanents are given. Also, the
adjiont matrices of matriecs over $R$ are considered. Partial results obtained
in this paper generalize the corresponding ones on fuzzy matrices, on lattice
matrices and on incline matrices.
