Concept

Ideal (order theory)

Related lectures (31)

Primary Decomposition: Understanding Schemes Log in to Mediaspace to watch this video

Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.

Chinese Remainder Theorem Log in to Mediaspace to watch this video

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

Tangent Spaces in Algebraic Geometry Log in to Mediaspace to watch this video

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Factorisation in PIDs Log in to Mediaspace to watch this video

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

Fractions of Rings Log in to Mediaspace to watch this video

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Dimension Theory of Rings Log in to Mediaspace to watch this video

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

Primary and Secondary Ideals Log in to Mediaspace to watch this video

Covers the concept of primary and secondary ideals, focusing on uniqueness and invariance properties.

Separable Extensions: Dedekind Rings Log in to Mediaspace to watch this video

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Rings: Operations and Ideals Log in to Mediaspace to watch this video

Covers the operations and properties of rings, focusing on ideals and quotients.

Primary Decomposition in Rings Log in to Mediaspace to watch this video

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

Regular Implicit Functions Log in to Mediaspace to watch this video

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.