Lecture
Rings and Fields
Related lectures (169)
Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Ideals and Representations
Covers ideals, representations, modules, and maximal ideals in associative algebras.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Chinese Remainder Theorem: Rings and Fields
Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
Weyl character formula
Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
Group Algebra: Maschke's Theorem
Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
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.
Chinese Remainder Theorem: Euclidean Domains
Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.