A semiring is a binary system $(S, +, imes)$ such that (S, +) is an Abelian monoid (identity 0), (S,x) is a monoid (identity 1), $ imes$ distributes over +, 0 $ imes s s imes 0 = 0$ for all s in S, and $1 eq 0$. Usually S denotes the system and $ imes$ is denoted by juxtaposition. If $(S, imes)$ is Abelian, then S is commutative. Thus all rings are semirings. Some examples of semirings which occur in combinatorics are Boolean algebra of subsets of a finite set (with addition being union and multiplication being intersection) and the nonnegative integers (with usual arithmetic). The concepts of matrix theory are defined over a semiring as over a field. Recently a number of authors have studied various problems of semiring matrix theory. In particular, Minc [4] has written an encyclopedic work on nonnegative matrices.