Concept

Dimension theory (algebra)

Related lectures (9)

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Complex Eigenvalues Appendix

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

Dimension Theory of Rings

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

Factorisation: The Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Complex Factorization Examples

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

Linear Differential Equations with Constant Coefficients

Explores linear differential equations with constant coefficients and roots implications in determining solutions.

Principle of Superposition in Differential Equations

Explores the principle of superposition in differential equations and the fundamental theorem of algebra.