Lectures related to Localization (commutative algebra)

Localization in Algebra

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

Surface Analysis: SIMS Examples

Explores surface analysis examples using SIMS, covering segregation, cleaning, and depth profiling of materials.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.

Abélianization: Fundamental Groups

Explores abélianization of fundamental groups in commutative spaces with examples and proofs.

Modular Arithmetic: Operations and Properties

Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.

Modular Arithmetic: Properties and Examples

Covers modular arithmetic properties, computation examples, and commutative rings.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.

Lagrange Theorem: Equivalence Relations

Explores Lagrange's theorem in commutative groups and the concept of equivalence relations, demonstrating their practical applications.

Isomorphism: Order of Group Elements

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Polynomials: Rings and Operations

Covers the basics of polynomials, focusing on rings, operations, and properties.

Commutation Groups: Euler's Totient Function

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Finite Fields and Vector Spaces

Explores finite fields, vector spaces, commutative groups, and field properties, highlighting their significance in coding theory and algebraic computations.

Chinese Remainder Theorem

Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Fractional Elements and Equivalence Relations

Explores fractional elements, equivalence relations, and injective mappings in commutative rings.

Boolean Algebra: Properties and Optimization

Covers Boolean algebra properties, optimization techniques, and the importance of valid groups in Karnaugh maps.

Commutative Rings and Fields

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

System Composition

Explains how systems are composed in parallel or series.

Integrity in Algebra

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

Multiplication: Properties and Definitions

Explains the definition and properties of integer multiplication in various scenarios.