Some Research Progress of Linear Systems Over Semirings

Linear systems over semirings, which generalizes classical linear systems, fuzzy relational equations, linear systems over max-plus algebras and linear algebras over inclines et al, attracts increasing attention all over the world recently. This paper surveys some research progress of linear systems over semirings made by researchers around the world. Its content includes the problem arisen, a semilinear space, the McCoy rank of a matrix and the generalized Cramer's rule and so on.