Concept

Commutative ring

Related lectures (30)

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers commutativity in rings, evaluation options, and formal linear combinations.

Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.

Polynomials: Rings and Operations

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

Primary Decomposition in Commutative Rings

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

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Isomorphism: Order of Group Elements

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

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Multiplication: Properties and Definitions

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

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.

Natural Numbers

Covers the concept of natural numbers, including properties like commutativity and associativity.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Ideals in Commutative Rings

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

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Homomorphisms and Projective Resolutions

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Abélianization: Fundamental Groups

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

Fractional Elements and Equivalence Relations

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