Primary Decomposition in Commutative Rings

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Dimension Theory of Rings

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

Idempotent Elements and Central Orthogonal

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.

Algebraic Geometry: Localization and Prime Ideals

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

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Chinese Remainder Theorem

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

Division Rings and Ideals

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Primary Decomposition in Rings

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

Ideals in Commutative Rings

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