Algebraic Geometry: Rings and Bodies

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Division Polynomials: Theorems and Applications

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Chinese Remainder Theorem: Euclidean Domains

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

Algebraic Geometry

Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, cyclic unit groups, and field construction.

Construction of Quotient Rings

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

Polynomial Factorization over Finite Fields

Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.

Ring Structure: Polynomials and Coefficients

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Decimal Expansion: Division and Periodicity

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.