Rings and Fields

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Related lectures (32)

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

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Ideals in Commutative Rings

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Division Rings and Ideals

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

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.

Fractions of Rings

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

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.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Affine Algebraic Sets

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

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