Additivity of Dimension & Height

Related lectures (32)

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

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

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

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

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

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

Discusses irreducible factors in rings and the properties of Noetherian rings.

Covers ideals, representations, modules, and maximal ideals in associative algebras.