Ring of Polynomials: Coefficients and Multiplication

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (31)

Integrity in Algebra

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

Algorithms for Big Numbers: Z_n and Orders

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Polynomials: Definition and Operations

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Geometric Sequences: Recurrence System

Covers geometric sequences and recurrence systems to find sequence terms and patterns.

Group Algebra: Maschke's Theorem Log in to Mediaspace to watch this video

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

Localization in Algebra Log in to Mediaspace to watch this video

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Polynomials: Definitions and Operations Log in to Mediaspace to watch this video

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Module Theory: Definitions and Examples Log in to Mediaspace to watch this video

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

Chinese Remainder Theorem: Rings and Fields Log in to Mediaspace to watch this video

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

Ring Theory: Sub-rings and Morphisms Log in to Mediaspace to watch this video

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

Ideals and Representations Log in to Mediaspace to watch this video

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Schur's Lemma and Representations Log in to Mediaspace to watch this video

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

Algebraic Structures of Morphism Spaces Log in to Mediaspace to watch this video

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Ring Theory: Definitions and Examples Log in to Mediaspace to watch this video

Introduces ring theory, covering definitions, examples, and subrings criteria.

Linear Algebra: Modules and Endomorphisms Log in to Mediaspace to watch this video

Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.

Construction of Quotient Rings Log in to Mediaspace to watch this video

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

Division Rings and Ideals Log in to Mediaspace to watch this video

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

Idempotent Elements and Central Orthogonal Log in to Mediaspace to watch this video

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Page 1 of 2