Abebaw Tilahun (PhD)Lakew Zenebe2018-07-192023-11-042018-07-192023-11-042016-07http://etd.aau.edu.et/handle/123456789/9483Certain techniques fundamental to the study of algebra. One of such techniques is the construction of a quotient set of an algebraic structure by a means of an equivalence relation on the given set. Based on this, we construct a quotient subtraction algebra, which plays a crucial role in the study of algebra. In this project work, we will introduce the notion of subtraction algebra, which is an algebraic structure on a set with a binary operation, usually called subtraction. To define subtraction algebra, we use the the concept of equivalence relation, subtraction algebra and ideal of subtraction algebra to define a quotient subtraction algebras and study its properties. The idea of isomorphism theorems of other algebraic structures is used to define isomorphism theorems of quotient subtraction algebras.enQuotient SubtractionThesis