Algebra Review: Rings, Fields, and Groups

Related lectures (31)

Page 3 of 4

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Explores the symmetric group, emphasizing cycle notation and group properties.

Explores operations on ideals and structure theorems in commutative rings.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

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

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

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.