E-Invertible Matrices Over Two Classes Of Semirings

Matrices over a semiring are one of the important research contents of algebra.Because of its wide application value,it has been paid more and more attention by scholars.e-Invertible matrices over a commutative antiring and strongly e-invertible matrices over a commutative semiring are studied in this dissertation.The main results are as follows:First,e-invertible matrices over a commutative antiring are discussed.By studying the properties of e-invertible matrices,some necessary and sufficient conditions of e-invertible matrices are given from the different views.Moreover,the maximal subgroup of e-invertible matrix semigroup is investigated and the semidirect product decomposition of maximal subgroup is obtained.Second,block matrices and strongly e-invertible matrices over a commutative semiring are studied.The necessary and sufficient conditions of block matrices as e-invertible matrices are given,and the relations between e-invertible matrices and strogly e-invertible matrices are revealed.Furthermore,the properties and equivalent conditions of strongly e-invertible matrices are obtained.