A Note of The Linear Equation AX = B with Multiplicatively-Reguler Matrix A in Semiring

Ariyanti, Gregoria (2019) A Note of The Linear Equation AX = B with Multiplicatively-Reguler Matrix A in Semiring. A Note of The Linear Equation AX = B with Multiplicatively-Reguler Matrix A in Semiring, 1366 (012063). pp. 1-6. ISSN pISSN: 17426588, eISSN: 17426596

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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 su�cient condition of semiring. Given a matrix A with the right complement matrix Ar satis�es AAr = 0. The su�cient condition of the linear equations system AX = B has a solution is there exist a matrix B satis�es AA�B = B and a matrix A has a right complement matrix Ar.

Item Type:	Article
Subjects:	Widya Mandala Catholic University on Madiun Campus > Faculty of Teacher Training and Education > Mathematics Education Study Program
Divisions:	Journal Publication
Depositing User:	F.X. Hadi
Date Deposited:	05 Jul 2023 02:51
Last Modified:	01 Aug 2023 05:47
URI:	http://repository.ukwms.ac.id/id/eprint/35449

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