Abstract Algebra: Exam 3 Review, Overview of Divisibility in Integral Domains, Ring Homomorphisms

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We review for abstract algebra exam 3 by mostly focusing on providing an overview of the topics on divisibility in integral domains. This includes: 1) the definitions of irreducible elements and prime elements, 2) the fact that every prime is irreducible, 3) every irreducible is prime in a principal ideal domain (PID), 4) every principal ideal domain (PID) is a unique factorization domain (UFD), 5) every Euclidean domain (ED) is a principal ideal domain (PID) and unique factorization domain, and 6) the fact that Z[sqrt(-5)] is not a unique factorization domain. We also look at old exam questions related to ring homomorphisms and finite Abelian groups.

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MuhammadUsman-jein