Lectures in course MATH-215: Algebra III - rings and fields

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

Covers commutativity in rings, evaluation options, and formal linear combinations.

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

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

Covers the operations in rings, ideals, classes, and quotient rings.

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

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

Explores the calculation of generators of ideals and their significance in mathematical operations.

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

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Explores Chinese idempotent constructions and their properties, including ideals and product characterization.

Covers the definition and properties of enclidian functions, including uniqueness and applications in mathematical structures.

Explores operations on ideals and structure theorems in commutative rings.

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

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

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Explores irreducibility criteria in rings, emphasizing linear and reducible polynomials.

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.