Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 2 2026 04 01 COMMUTATIVITY FOR THE WEAKLY RIGHT CANCELLATIVE SEMIRINGS: AN ENTIRELY NOVEL CATEGORY OF SEMIRINGS AND A WEAK CONDITION FOR COMMUTATIVITY RESEARCH 197 208 3732 10.22044/jas.2024.13745.1764 EN Kamal Charrabi Charrabi Department of Mathematics, Faculty of Sciences, Moulay Ismaïl University, P.O. Box 11201, Meknes, Morocco Abdellah Mamouni Department of Mathematics, Faculty of Sciences, Moulay Ismaïl University, P.O. Box 11201, Meknes, Morocco Bader Nejjar Laboratory of Innovant Technologies, High School of Technology, SMBA University, P.O. Box 2427, Fes, Morocco Journal Article 2023 10 21 The goal of this study is to provide an innovation for commutativity research that is less than the strong condition prime ring. This paper will describe weakly right cancellative semirings and examine how commutativity and generalized derivations apply to this class of semirings. A detailed explanation and classification of some of these generalized derivations are also included. Semiring cancellative semiring derivation generalized derivation https://jas.shahroodut.ac.ir/article_3732_7b260ccd1078584ca0a4b8f596376e64.pdf