This course on Abstract Algebra Integral Domains covers the following learning outcomes and goals: understanding the field of fractions of an integral domain, identifying irreducibles and primes in integral domains, exploring unique factorization domains and principal ideal domains, recognizing the properties of Euclidean domains, and analyzing the relationship between PIDs and UFDs. The course teaches students the skills to work with integral domains, PIDs, and Euclidean domains. The teaching method involves theoretical explanations and examples to illustrate key concepts. The intended audience for this course includes students and professionals interested in advanced algebraic structures and properties.
Overview
Syllabus
Abstract Algebra | The field of fractions of an integral domain..
Abstract Algebra | Irreducibles and Primes in Integral Domains.
Abstract Algebra | Introduction to Unique Factorization Domains.
Abstract Algebra | Introduction to Principal Ideal Domains (PIDs).
Abstract Algebra | Every PID is a UFD..
Abstract Algebra | Introduction to Euclidean Domains.
Abstract Algebra | If D is a UFD then D[x] is a UFD..
Abstract Algebra | Summary of Integral Domains.
Abstract Algebra | A PID that is not a Euclidean Domain.
Abstract Algebra | A PID that is not a Euclidean Domain.
Abstract Algebra | Ideals of quotients of PIDs.
Taught by
Michael Penn
