Lectures related to Algebras and Field Extensions

Introduces Lie algebras, vector spaces with a special bracket operation.

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Covers the properties of the algebra of matrices and related concepts.

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

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

Covers linear applications, matrices, transformations, and the principle of superposition.