Browsing by Author "Lakew Zenebe"
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Item Quotient Subtraction Algebra(Addis Ababa University, 2016-07) Lakew Zenebe; Abebaw Tilahun (PhD)Certain 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.