Lectures related to Ringed space

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

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

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.