Order (ring theory)

Related lectures (16)

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Discusses Fermat's equation and Gaussian integers' properties.

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Explores the properties of commutative rings and integral domains in algebra.

Covers the properties of the algebra of matrices and related concepts.

Covers the basics of solving polynomial equations, historical methods, matrix properties, imaginary numbers, and subrings in matrix algebras.

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

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

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

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

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

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