Quotient Subtraction Algebra
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Date
2016-07
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Addis Ababa University
Abstract
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.
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Quotient Subtraction