Lectures related to Irreducible Polynomials and Finite Fields

Irreducible Polynomials and Finite Fields

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

Chinese Remainder Theorem: Rings and Fields

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

Algebra Review: Rings, Fields, and Groups

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Rings and Fields: Principal Ideals and Ring Homomorphisms

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Introduction to Finite Fields

Covers the basics of finite fields, including arithmetic operations and properties.

Algebraic Geometry: Rings and Bodies

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

Properties of Euclidean Domains

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

Properties of Euclidean Domains

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

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Irreducible Polynomials: Degree and Roots

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Finite Fields and Group Theory

Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Finite Fields: Construction and Properties

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Dimension Theory of Rings

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Finite Fields: Properties and Applications

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Generalized Integrals: Elementary Cases

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

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