### KARAKTERISASI MATRIKS ATAS SEMIRING DALAM SISTEM PERSAMAAN LINEAR

#### Abstract

*A Semiring is an algebraic structure * * such that * * is a commutative Semigroup with identity element 0, * * is a Semigroup with identity element 1, distributive property of multiplication over addition** and multiplication by 0 as a absorbent element in * *. A linear equations system over a Semiring * * is a pair * * where * * is a matrix with entries in * * and * * is a vector over * *. In this paper will be described characterization of matrix * * that satisfies * *,** with* *,* *as necessary or sufficient conditions of solution of linear equations system over Semiring * *. ** For a matrix * * that satisfies * , *a linear equations system * *has solution* *with arbitrary * * in * * if and only if* .

#### Keywords

semiring, linear equations system, matrix

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**LP3M Unika Widya Mandala Madiun**

lp3m@widyamandala.ac.id