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Abstract AlgebraIntegral Domains are essentially rings without any zero divisors. These are useful structures because zero divisors can cause all sorts of problems. They complicate the process of solving equations, prevent you from cancelling common factors in an equation, etc. In this lesson we introduce the idea of an integral domain, talk about solving an equation over rings with and without zero divisors, and show how the cancellation property does hold in an integral domain.

Integral Domains are essentially rings without any zero divisors. These are useful structures because zero divisors can cause all sorts of problems. They complicate the process of solving equations, prevent you from cancelling common factors in an equation, etc. In this lesson we introduce the idea of an integral domain, talk about solving an equation over rings with and without zero divisors, and show how the cancellation property does hold in an integral domain.

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Course Description

Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.