Related lectures (32)
Primary Decomposition: Noetherian Ideal
Covers primary decomposition in Noetherian ideals and unique primary ideals.
Dedekind Function: Analytic Continuation and Euler Product Formula
Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.
Dimension of Algebraic Variety
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Prime ideals and local rings
Covers the concept of prime ideals and local rings, emphasizing their importance.
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.
Commutative Algebra: Recollections
Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.
Idempotent Elements and Central Orthogonal
Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.
Algebraic Varieties: Projective Sets and Topology
Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.
Affine Varieties and Hypersurfaces
Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

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