Modular Arithmetic: Properties and Examples

Related lectures (29)

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

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

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

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

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

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