Algebra

Related lectures (25)

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

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

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

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

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

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

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

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers the properties of finite dimensional algebras and non-semisimple representations.

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

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

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

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