Module Theory: Definitions and Examples

Related lectures (32)

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

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

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

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

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

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Covers the operations in rings, ideals, classes, and quotient rings.

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

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

Introduces matrix algebra operations and their properties, including commutativity and distributivity.