Rings and Ideals

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Related lectures (32)

Properties of Euclidean Domains

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

Ring Homomorphisms and Ideals

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

Construction of Quotient Rings

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

Ideals and PPCM

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

Integrity in Algebra

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

Prime ideals and local rings

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

Polynomials on a Field: Properties and Applications

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

Group Algebra: Maschke's Theorem

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

Irreducible Factors and Noetherian Rings

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

Affine Algebraic Sets

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

Symbolic Powers: Interpretation and Applications

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

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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