Some Studies On U-product And Singularity Of Matrices Over Commutative Semirings

In this thesis,we study the u-product and the singularity of matrices over commutative semirings.First,we introduce the concept of u-product and standard orthogonal sets in the case of u-product.Then,we discuss the properties of orthogonal sets and orthogonal semimodules in the definition of u-product.At the same time,we study the expansion of standard orthogonal sets in the case of u-product.Finally,we study the equivalent conditions of semilinear row singular and column singular,and the equivalent conditions of semilinear row singular and d-singular.The sufficient conditions for a semiring to satisfy the semilinear condition are discussed.