Seminear Module over Seminear-ring Fitriana Hasnani(a*), Meryta Febrilian Fatimah(b), Nikken Prima Puspita(c)
a) Graduated student of The Magister of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia
*fitriana.hasnani[at]gmail.com
b) Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Sulawesi Barat, Jl. Prof. Dr. Baharuddin Lopa, S.H, Majene 91412, Indonesia
c) Mathematics Department, Faculty of Sciences and Mathematics, Universitas Diponegoro, Jl. Prof. Jacub Rais, Semarang 50275, Indonesia
Abstract
Let S be a semigroup. The structure of seminear modules over a seminear-ring is motivated by the properties of semigroup S and the set of natural number N with addition and left multiplication operation. In this paper, we introduced the new algebraic structure i.e., seminear modules over a seminear-ring. Seminear modules over a seminear-ring is a generalization of some algebraic structure such as modules over a ring, semimodules over a semiring, near modules over a near-ring. Moreover, we also gave some examples as the existence of our new algebraic structure. According with to in the module theory, it is shown also that the intersection of two subseminear module is a subseminear module and the sum of two sub modified seminear module is a sub modified seminear module.
Keywords: module, seminear module, seminear-ring, subseminear module, left multiplication
