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 .