Lectures related to Ring Theory: Sub-rings and Morphisms

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

Discusses irreducible factors in rings and the properties of Noetherian rings.

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

Discusses Fermat's equation and Gaussian integers' properties.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

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

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Explores operations on ideals and structure theorems in commutative rings.

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.