Lectures related to Localization in Algebra

Explores the properties of commutative rings and integral domains in algebra.

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

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

Introduces the definition and examples of A-modules, including sub-modules and ideals.

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.

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

Covers the ring of polynomials, focusing on coefficients and multiplication.

Explores modules over a ring, injective morphisms, isomorphisms, and canonical groups.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.