Lectures related to Rings and Ideals

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

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Explores the construction of quotient rings and the properties of well-defined operations within rings.

Covers the concept of ideals in polynomial rings and their properties.

Explores the properties of commutative rings and integral domains in algebra.

Covers the concept of prime ideals and local rings, emphasizing their importance.

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Discusses irreducible factors in rings and the properties of Noetherian rings.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.