Dimension Theory of Rings

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Related lectures (32)

Page 3 of 4

Rings and Fields: Principal Ideals and Ring Homomorphisms

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Properties of Euclidean Domains

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Chinese Remainder Theorem

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

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Commutative Algebra: Recollections

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Primary Decomposition in Rings

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Ring Operations: Ideals and Classes

Covers the operations in rings, ideals, classes, and quotient rings.

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Properties of Finite Dimensional Algebras

Covers the properties of finite dimensional algebras and non-semisimple representations.