Algebra Review: Rings, Fields, and Groups

Related lectures (31)

Page 2 of 4

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

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

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.