Teshome, Zelalem(PhD)Tilahun, Abayneh2018-07-112023-11-042018-07-112023-11-042016-09-09http://etd.aau.edu.et/handle/123456789/7792This project deals with introduction of subtraction algebra, weak subtraction algebra and their the properties.order systems and ideals of a weak subtraction algebra and a subtraction algebra will be introduced.the concept of xed map in weak subtraction algebra will be discussed. Conditions for an ideal to be irreducible will be provided. More over, relations between ideals and order systems are givenenOrder SystemsIdeals and RightThesis