Concept
Polynomial ring
Related lectures (214)
Modular Arithmetic: Operations and Properties
Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.
Modular Arithmetic: Properties and Examples
Covers modular arithmetic properties, computation examples, and commutative rings.
Ring Constructions: Structure Theorems
Explores operations on ideals and structure theorems in commutative rings.
Polynomials: Roots and Factorization
Covers polynomial roots, factorization, and unique representation through examples of polynomial division with remainders.
Commutativity in Rings
Covers commutativity in rings, evaluation options, and formal linear combinations.
Cyclic Subspace Decomposition
Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.
Ordinary Differential Equations: Definitions and Solutions
Explores Ordinary Differential Equations definitions, solutions, polynomial degrees, autonomous solutions, maximal solutions, and Cauchy's problem.
Algebraic Closure of Qp
Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.
Polynomial Factorization: Field Approach
Covers the factorization of polynomials over a field, including division with remainder and common divisors.
Properties of Euclidean Domains
Covers the properties of Euclidean domains and irreducible elements in polynomial rings.