Abstract Algebra, Lec 30A: Divisibility in Integral Domains: Associates, Irreducibles, Primes, Norms

Abstract Algebra, Lecture 30A

(0:00) The lectures that are left.
(0:35) Topics for the day and words of encouragement.
(1:29) Rational root theorem statement.
(3:03) Creating a textbook or exam problem where the Rational Root Theorem can be used.
(3:59) Rational root theorem example.
(12:04) Associates, irreducibles, primes in integral domains (think about units in Z, Z[i], Z[x], F[x], and F to help).
(23:38) Basic facts relating associates, irreducibles, and ideals in the integral domain.
(30:39) Integers adjoined by square roots and a norm defined on such a ring, including fundamental properties of such a norm.
(35:28) Example of an irreducible that is not prime in Z[sqrt(-3)].

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