Local Rings and Minimal Primes

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Related lectures (32)

Page 3 of 4

Regularity and Noetherian Local Rings

Covers the concepts of regularity and Noetherian local rings in algebraic structures.

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Number Theory: Primes

Covers the definition of primes, the Fundamental Theorem of Arithmetic, and Euclid's Theorem.

Chinese Remainder Theorem: Rings and Fields

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

Primes: Fundamental Theorem and Sieve of Eratosthenes

Explores primes, the Fundamental Theorem of Arithmetic, trial division, the Sieve of Eratosthenes, and Euclid's Theorem.

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.

Number Theory: More Facts about Primes

Covers the distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

Module Theory: Chain Conditions

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.