Open AccessA Note of The Linear Equation AX = B with Multiplicatively-Reguler Matrix A in Semiring
Author(s) -
Gregoria Ariyanti
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1366/1/012063
Subject(s) - semiring , mathematics , complement (music) , matrix (chemical analysis) , generalization , inverse , ring (chemistry) , pure mathematics , element (criminal law) , algebra over a field , discrete mathematics , combinatorics , mathematical analysis , geometry , biochemistry , materials science , organic chemistry , complementation , composite material , gene , phenotype , political science , law , chemistry
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 .