Lectures related to Field of Fractions: Definition and Properties

Commutative Rings and Fields

Covers commutative rings, fields, injective morphisms, characteristic, Frobenius, and binomial theorem.

Canonical Embedding: Fields and Lattices

Explores canonical embedding of #-fields, lattices, and finiteness of class groups.

Ring Theory: Morphisms and Isomorphisms

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Algebraic Structures of Morphism Spaces

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

Module over a Ring

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

Injective Morphisms in Mathematics

Introduces injective morphisms and vector spaces with examples and verification methods.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Sheafification of Presheaves

Covers the sheafification process of presheaves, emphasizing injectivity and surjectivity.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Finite Maps: Morphism of Schemes

Covers morphism of schemes, affine covering, integral homomorphism, and properties of finite maps.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Equivalence Classes and Relations

Covers equivalence classes, relations, quotient sets, and functions properties.

Local Noetherian Rings

Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.

Group Theory: Part 2

Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

Morphisms between Affine Varieties

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Dimension Theory of Rings

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Integers and Rings

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.