Lectures related to Multiplicatively closed set

Covers integral extensions in rings and modules, discussing properties and providing illustrative examples.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Discusses Fermat's equation and Gaussian integers' properties.

Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.

Covers the concept of prime ideals and local rings, emphasizing their importance.

Discusses norms, distances, and the classification of open and closed sets in mathematical analysis.

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.