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Lecture
Additivity of Dimension & Height
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Related lectures (32)
Algebraic Quotients
Covers the concept of algebraic quotients in the context of a-variety.
Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Factorisation in PIDs
Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Ideals in Commutative Rings
Covers the concept of ideals in commutative rings and their role in ring homomorphisms.
Fermat's Equation: Integral Solutions and Gaussian Integers
Discusses Fermat's equation and Gaussian integers' properties.
Principal Ideal Domains: Structure and Homomorphisms
Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.
Localization in Algebra
Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.
Dimension of Algebraic Variety
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Commutative Algebra: Recollections
Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.
Simple Modules: Schur's Lemma
Covers simple modules, endomorphisms, and Schur's lemma in module theory.
Factorisation in Dedekind Ring
Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.
Integrity in Algebra
Explores the properties of commutative rings and integral domains in algebra.
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