Concept

Irreducible polynomial

Related lectures (31)

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

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Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Algebraic Geometry

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

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

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.

Ramified Extensions: Eisenstein Polynomials

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Generalized Integrals: Elementary Cases

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

Algebraic Closure of Qp

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

Properties of Euclidean Domains

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

Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Integration of Simple Elements

Covers the integration of simple elements and limit expansions with examples.

Algebraic Extensions

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.

Polynomial Factorization over a Field: Eigenvalues

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Built-In Self-Test (BIST): Techniques and Implementations

Explores Built-In Self-Test (BIST) techniques in VLSI systems, covering benefits, drawbacks, implementation details, and the use of Linear Feedback Shift Registers (LFSRs) for test pattern generation.

Irreducible Polynomials: Degree and Roots

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

Complex Factorization Examples

Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.

Polynomial Factorization: Field Approach

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Algebraic Curves: Normalization

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