Ring Constructions: Structure Theorems

Related lectures (32)

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Explores rings, fields, ideals, and their properties in algebraic structures.

Covers the operations and properties of rings, focusing on ideals and quotients.

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

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