Plane Curves: Singular Points and Multiplicities

Related lectures (32)

Page 3 of 4

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

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

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

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

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

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

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

Covers the representation of plane curves and the nature of obtained curves.