A Note of The Linear Equation AX = B with Multiplicatively-Reguler Matrix A in Semiring
Gregoria Ariyanti · Journal of Physics Conference Series · 2019
Abstract Semiring is a form of generalization of the ring, where one or more conditions in the ring are removed. An element a is called multiplicatively-regular if there is x so axa = a. In real number algebra, a system of linear equations AX = B has a singular solution if a matrix A has an inverse. Elements of semiring which does not a zero element have no inverse of addition. By reviewing matrix A as a multiplicatively-regular, it is develop of necessary or sufficient condition of semiring. Given a matrix A with the right complement matrix A r satisfies AA r = 0. The sufficient condition of the linear equations system AX = B has a solution is there exist a matrix B satisfies AA [openbullet] B = B and a matrix A has a right complement matrix A r .