Local Noetherian Rings

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Related lectures (32)

Division Rings and Ideals

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

DVR and Irreducible Plane Curves

Explores Discrete Valuation Rings and their role in irreducible plane curves.

Affine Algebraic Sets

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

Properties of Euclidean Domains

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Chinese Remainder Theorem: Euclidean Domains

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Division Rings and Ideals

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Morphisms between Affine Varieties

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Algebraic Geometry: Rings and Bodies

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

Irreducible Factors and Noetherian Rings

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

Integers and Rings

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

Homogeneous Ideals and Regular Rings

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

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