Abstract algebra

Related lectures (31)

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

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

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

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Covers the properties of finite dimensional algebras and non-semisimple representations.

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

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

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.