On invertible matrices over commutative semirings

摘要

In this article, the invertible matrices over commutative semirings are studied. Some properties and equivalent descriptions of the invertible matrices are given and the inverse matrix of an invertible matrix is presented by analogues of the classic adjoint matrix. Also, Cramer's rule over a commutative semiring is established. The main results obtained in this article generalize the corresponding results for matrices over commutative rings, for lattice matrices, for incline matrices, for matrices over zerosumfree semirings and for matrices over additively regular semirings.